I have a level 3 Half Elf Swashbuckler mainly for DPR and some skill utility and a bit of a face (she uses deception a lot).

Long campaign unless she dies will probably get to about level 15.

Most of the time she will dual wield short swords going in to attack and then retreat,  

Abilities are Str=8 Dex=16 Con=14 Int=10 Wis=14 Cha=14

Fairly sure at level 4 I will go ASI Dex but am am totally uncertain what to do after that:

I've played a reasonable amount but never multi-classed but am considering whether to MC into Fighter one possibility is to start taking fighter here:

1 Level Fighter:  Two weapon fighting is the obvious fighting style but being close to the front line I was wondering if defence would be better, or picking up a rapier, shield and the duelling style. I suspect second wind will not be used much in combat as I have so many options competing for my bonus action and the amount of healing might not be enough to make me survive another hit. So it will just give me a few extra HP between battles.

2nd level of fighter: Actions surge would be great for when I miss on my Action and bonus action and still have a chance to sneak attack.  

3rd level fighter. I am thinking battle master would be a great supplement to a rogue for Precision attack, Riposte and trip attack is this right?

4th Level: I wouldn't want to be an ASIs/ Feat down getting a 4th level of fighter would allow me to get max Dex at level 8 instead on 11. (Or would a feat such as dual wielder better?)

5th Level: 2nd attack, another chance to land sneak attack

6th Level: Again allows me to Get an ASI / Feat 3 levels early

Can't see me going any further than this

At Rogue 5 I would get Uncanny dodge and an extra sneak attack die should I get that before considering fighter levels?

I am aware the more fighter levels I get the weaker my sneak attack will be and the later I get expertise, evasion, panache and reliable so while all the fighter feature look great would I be gimping the rogue?    

The Dual Wielder feat is only one AC behind a Shield, but letting you atack with your bonus action gives you more certainty that you can land a hit to deliver Sneak Attack every round. That said, Two Weapon fighting style only lets you add +3-5 damage on that offhand attack, which isn't really where Rogue dpr comes from, so if you want to take Defensive fighting style you absolutely can! Another thing you might consider if you want more defense is taking the Defensive Duelist feat; it steps on Uncanny Dodge a little bit, but depending on whether your DM lets you know what enemies rolled when they attack to hit you, using a reflex to make an attack miss is strictly superior to using it to take half damage from that attack. 

Battle Master is an outstanding subclass to supplement you, since it lets you debuff your opponents with Prone, Fear, push them, make your attacks more accurate or reachy, etc. Other good options include Champion (19-20 crits, but kinda boring) or Samurai (bonus action to get advantage on your attacks that round, which isn't always necessary for you to get a crit off, but is still a pretty great way to ensure you hit things). 

Taking Fighter to 8 instead of 6 is ultimately at 20: (1) one more feat, (2) one more fighter subclass feature (only Samurai's is good), (3) but lose Blindsense, (4) lose 1d6 SA, (5) and lose Elegant Maneuver (no big deal). You're probably not building for 20 though, the real impact is just delaying when you get to Rogue 5 (uncanny dodge and +1d6 SA) and etc. So yeah, stopping at Fighter 6 makes sense, and you may not even want to go all the way to Fighter 6 before going back to Rogue to alternate (though I would, getting Dex to 20 two levels earlier than going back to Rogue for Uncanny Dodge would allow is maybe worth it)

I'd suggest this order:

• Rogue to 4, +2 Dex to 18
• Fighter (Battlemaster) to 4, Dual Wielder (increases your dpr and gives you +1 AC, worth putting off Dex two more levels) (character level 8)
• Fighter to 6, +2 Dex to 20 (character level 10)
• Rogue to 8+, no more ASI but feats may include Inspiring Leader, Defensive Duelist, Mobile, Lucky, Elven Accuracy, Martial Adept, Prodigy, or Wood Elf Magic

The basic Rogue class is every bit as strong as the Fighter class, IMHO. Every level of Fighter you take is a level of Rogue lost. If you're currently at 3rd level, you should look at what you're getting at upcoming Rogue levels and decide if it's worth delaying for a level of Fighter.

4th level: ASI/Feat. Rogue wins.

5th level: Uncanny Dodge. Rogue wins.

6th level: Expertise. Uh, maybe? But if you like the Deception skill, then Rogue wins. (Choose Persuasion and Deception to power up your 9th level ability)

7th level: Evasion. Rogue wins easy.

8th level: ASI/Feat #2. Rogue wins.

9th level. Panache. Advantage on Deception checks for 1 minute. Rogue wins.

10th level. Bonus ASI/Feat! Rogue wins.

11th level. Reliable Talent. Rogue wins.

12th level. ASI/Feat. Rogue wins; if you stay single classed, the Rogue has only one less ASI than the Fighter.

13th level. Elegant Maneuver. This is your first real "dud" IMHO. You might want to go Fighter for a level or three here. But the Rogue's level 14 and 15 features (Blindsense, Slippery Mind) would be hard to pass up, IMHO.

As you can imagine, I'm not a huge fan of multiclassing when it comes to Rogues.

You're vastly underestimating the utility of those Battlemaster maneuvers, and of Action surge, but yes the feats and fighting style from Fighter are not particularly better than the Feats and rogue features. It just comes down to how important maneuvers are for you... but maneuvers give you so much field control, and tack on their own bonus damage which compensates for lower SA, that I don't think OP is has cost himself much by going that route. 

Chicken

Some interesting thoughts:

For defensive duelist, using a reflex to make an attack miss is strictly superior to using it to take half damage from that attack is obviously true but having uncanny dodge halves the power of the feat  as you are only avoiding half the damage instead of the full amount that most characters get from it.

With only +2 Cha is inspiring leader worth it?

Mobile is another one I hadn't really extra movement is great, I am not sure how much difficult terrain we will come across and I already have fancy footwork

If I go battlemaster I will already have my 3 favourite manoeuvres is getting an extra superiority dice and a bit ore flexibility with manoeuvres worth a feat?

I don't think half elves are allowed to take wood elf magic but it they were you are right it would be great.

Lucky, Elven Accuracy and prodigy are definitely options for feats,

My backstory is I am a member for the city watch who has been studying the ways of the bad guys and I have a feature  that I can be passed off as one of their goons.  Actor could really help this as I could try to be one of their leaders and get the goons to do what I want. (Advantage  and Expertise should mean a high chance of success), If I also took Elven Accuracy I might be able to get my charisma to +3 (though the GM might rule elven accuracy a full feat I know he does this for one shots), if elven accuracy is ruled a full feat i would consider resilient Wis and an ASI to get them both up to 3 but I would get everything even again until level 16 if I get there

As someone who can stand up to a bit of melee but is very sneaky i will be spending some time a bit ahead of the rest of the party scouting ahead Alert could help a lot if I go into an ambush

 So you think once I have Dex maxed feats are better than increases to charisma, or con?

Jack

I haven't ruled out straight rogue but it isn't as obvious as you claim, if I start fighter at level 4 and take 6 levels:

PC level 5: Uncanny dodge v Fighting style and second wind  - OK rogue probably wins

PC6 Expertise v Actions surge  straight up fighter wins probably still wins when you include the sneak attack dice

PC7 Evasion v battle master  - Evasion is great when you have to make a Dex save but manoeuvres gives you a significant gain much more frequently I'd say fighter wins here 

PC8 ASI v ASI    - excluding sneak attack dice Tie, the loss of a SA die make this a win for the Rogue  

PC9 Panache v 2nd Attack   -  Panache is very situational, advantage on deception checks for 1 minute is great but you need ot be prepared for what to do after 1 minute when the NPC realised you tricked him into telling you what he wouldn't have done otherwise.  Fighter is the winner here

PC10 ASI v ASI   -  see level 8

PC11 Reliable v Uncanny dodge   -  Depends how combat oriented the campaign is I'll call this a tie

PC12 ASI v Expertise    -  Single class wins

PC13 Elegant Maneuver v Evasion   -  Multi class wins 

PC14 Blind-sense v  ASI   -  Multi Class wins

PC15 Slippery mind v Reliable   -  Depends on the campaign but I think multi class wins

PC16 ASI v ASI   -  tie

PC17: Master Duelist v Elegent Maneuver   -  probably go with single class here

Doubt I'll get further than this.   

I do think that Feats are better than ASI to your other stats, after 20 dex. +/- 2 to checks other than your attack and your AC are not going to feel like they have as big an impact at the table as having a new ability that marks you out as special. You probably won't feel "cool" for having 16 CHA instead of 14, but being able to do something special with Inspiring Leader or something else is going to put a real spotlight on you. 

Inspiring Leader twice per day (once after long rest, once after a short rest) at +0 CHA is Toughness for the whole party. For a four-person party at 4 it's 32 HP that doesn't need to be healed, saving spell slots, action economy, and close calls (equivalent of about 4 Cure Wounds by a competent caster). At level 20 it's 160 HP that doesn't need to be healed (the equivalent of about 18 Cure Wounds by a max stat caster, though there's probably more efficient healing by then). It's a feat that someone should have in every party, and your 14 Charisma doesn't hurt, and you're likely to have more free feats than others as a Rogue or Rogue/Fighter. Just food for thought.

Mobile is useful for lots of things: ensuring you can stay in melee range every round by giving you 10 extra feet or even difficult terrain clearing with a bonus Dash is a big one... but also, it lets you dart in and out of combat with a BBEG to deliver Sneak Attacks without having to commit to staying and being a target for them. That can be not only good for you, but also good for your party tank if they'd rather be the only thing left in melee combat with a foe they're trying to lock down, if they don't otherwise have a good taunt mechanic. 

The Martial Adept recommendation was really mostly about getting one more superiority die so that you have 4 instead of 3, but also two more maneuvers can also make you more flexibile. The maneuvers you "need" for yourself are probably Precision Attack (make sure you land that vital SA!), Pushing Attack (push off a cliff for massive damage, or ungrapple yourself, or flingsomeone out of position for your team to pounce, or escape the threat range of a counterattack!), and Trip Attack (set yourself and your whole team up for an entire round of advantage on attacks!).  Other nice maneuvers for yourself include Lunging Attack (meh, rarely if ever will you come up only 5 feet short of something), for board control include Disarming Attack (usually more for stealing plot devices than disarming weapons) and Menacing Attack (great hard board control, since if it sticks the DM must respect not coming nearer to you, and it debuffs their attacks for a round against the whole team), and for party support including Commander's Strike (more common for the fighter to give the rogue an attack with this than the other way around, but possibly useful sometimes) and Maneuvering Attack (very very likely to come up, frees your party up to play more aggressive by letting you save backliners without babysitting them). So yes, I'd say that learning two more maneuvers can expand your toolbox quite a bit.

I am surprised you don't mention riposte as a manouver that I need or even could be useful. I would have thought that would have a significant increase to the number of sneak attacks I get. 

I'd have thought pushing attack is quite situational I don't think I had ever fought a D&D battle where the bad guy was stand within 10 ft of a cliff, with fancy footwork I don't need it to avoid a counter attack either.   

I mentioned I was thinking of riposte, trip and precision as the 3 I would take, if I got two more they would probably be menacing and manoeuvring. In fact is ost of the party were ranged I would probably take menacing over trip.

I had forgotten Fancy Footwork, you’re right that Mobile is (half) redundant, my bad.

Riposte (1) requires you to stand still in melee and invite getting hit, which isn’t really your job; (2) only triggers if they miss, which they may well hit you or ignore you instead;  and (3) requires your reaction, which may not be available if you’ve already used it for uncanny dodge (or defensive duelist) or competes with your ability to use those later when you need them to live; and (4) expends a superiority die to MAKE an attack (which can miss and be wasted) instead of being used after you confirm a hit like the others I recommended, which is a big deal when you only have 3 dice.

Its fine on a tank fighter to up their dpr (maybe on a Sentinel to truly give a foe nothing they can do on their turn to avoid an OA), but it’s really probably not for you. Push Attack I like a lot as a way to break a grapple without spending an action to escape if nothing else, but if that’s not for you, but I would still take Menacing Strike or Commanders Strike to help your party out. Both of those can be used to save a party member in danger or offensively outmaneuver a foe, but Riposte is going to just result in a lot of “oh shoot, if only I hadn’t already...” moments.