I have a question I need some help with, in our campaign we have a situation where a character is carrying vital information that he is not willing to give up. Here is the situation, this character was taken prisoner by our local mystic, ok, she was able to perform a "mystic Charm" on him. Now, she then told this character that he had to do what she asked hince being charmed, but, she only stated to him that she was going to perform a "mind Meld" nhim, and asked if he understood her. His reply was simply "yes", this implied to me that he was willing to allow the meld. His argument is that he is charmed and that she cannot use a meld on a charmed subject because being charmed takes away his free will, thus a mind meld must be made on a "willing subject" . My argument is that since she did not ORDER him to allow the meld, she simply told him she was going to do one, and he replied yes, this tells me that some part of him was "willing" to allow it, I have ruled that the meld is to take place. Was I incorrect in doing so?

As a DM you decide effects in the world. Thus, you were correct.

That being said, I would take this out if character and ask if this is something the player is or is not willing to do and if not, why. 

You might have to retcon the encounter or work the failure into the story. Just remember, its your decision. 

TLDR: The mystic cannot access the memory.

My first question is why does the player not want to give up the information?
Are they just being difficult, or is it something with real reasons behind it, like its vital to their faction and they don't want to betray it.
If they are just being difficult, are there other ways to get the info that don't involve the player.

I am assuming for Mystic you are referring to the UA Mystic that WotC published. Lets take a look at the abilities:

Mystic Charm
As an action, you beguile one humanoid you can see within 120 feet of you. The target must succeed on a Charisma saving throw or be charmed by you until the end of your next turn.

Mind Meld
As a bonus action, you can communicate telepathically with one willing creature you can see within 120 feet of you. The target must have an Intelligence of at least 2, otherwise this talent fails and the action is wasted. This communication can occur until the end of the current turn. You don’t need to share a language with the target for it to understand your telepathic utterances, and it understands you even if it lacks a language. You also gain access to one memory of the target’s choice, gaining perfect recall of one thing it saw or did.

And last, the charmed condition

• A charmed creature can't attack the charmer or target the charmer with harmful abilities or magical effects.
• The charmer has advantage on any ability check to interact socially with the creature.

Charmed does not affect a creature's willingness on its own. It merely grants advantage to social checks. So Mystic Charm alone is not enough to allow Mind Meld to work.

In addition, the character can consent to Mind Meld, and the mystic still wouldn't get the information, as its the target's choice of what memory they share, and they are under no compulsion to share this specific information.

About the only thing I can think of that might work is Dominate Person but you need to be careful brute forcing a player character like this. It will probably make them really unhappy. So back to my original point, why don't they want to give up this information in the first place?

But if he is charmed and under the mystic's control, then couldn't she tell the character what information to reveal? She was not in any way forcing him to allow the meld, she simply asked him if he understood she was going to perform one, thus he answered yes, this indicates he is giving permission for the meld. I feel that since he is under her control, that he would have to reveal whatever information she seeks. As I understand it, a charmed person must obey the charmer ,thus she is telling him what information to reveal.  He has no control over that, only control over whether or not to allow the meld, and in my opinion, he did so.

Mystic Charm does not put the target under the mystic's control. It applies the charmed condition which does: The charmer has advantage on any ability check to interact socially with the creature.

Only Dominate effects allow total control, like the Dominate Person spell

Again too, why is this player reluctant to divulge this information?

Ok, so the entire event is invalid, since he is not under her control, she would need to use a different method to gain that sort of control over him such as like you said a dominate spell. If she did that, then she could order him to reveal the information right, even without using the meld?

Could she use "Dominate Person" to gain control of him, then tell him to allow the meld, and then tell him what info to release? Or would she not even need the meld?

Forcing the character to divulge information that the player doesn't want them too is a surefire way to get a player angry. Again, why does this character have information that they do not want to give up. There may be other ways to solve this without forcing a player against their will. Or is than an NPC mystic trying to get it for nefarious means?

Just Dominate Person alone would be enough.

Are we talking about two players where one try to force information from the other or an NPC trying to force information from a PC?

If it's an NPC, you could perhaps just rule that this NPC has powers that makes it work, just to get your campaign going. Basically make this a special ability of the NPC. I say perhaps, because I know some groups could react to this, some will not, depending on play style and "faith" in the DM.

If it's two players, I'll say it's time to talk to them.

The prisoner has a fair case if he actually was roleplaying when he said yes. If he claims so, and also he never meant to give the mystic access to the memory, I would give him the benefit of a doubt. It's been a misunderstanding, now it's cleared.

The final question - and perhaps problem if it's to PC's is of course why they are using such methods to gain vital information from each other. I won't say we haven't been there in some campaigns, but when you are there, you might have a problem down the road with a group that is splitting up...

It is two PCs, and the information is vital to the mystic to save her kingdom from control by the enemy, she needs to try and reveal a possible traitor. So it is vital she gets this info. It would not be a problem in the campaign because the information was proposed by the prisoner and the motion was set in play by him, he set things in motion so it should not cause any ill feelings, if he did not want the information to be obtained eventually, he should have been more cautious about revealing his possible intent. Apparently he had been communicating privately with other players who may or may not know of his actual plans. The mystic in question has extraordinary perception skills and she indicated she knows about a possible traitor and since she is certain she is able to trust all of the current members of the royal house, and since this prisoner is the newest member of said house, and since he had been acting in a suspicious manner, even communicating with the mystic privately, she had to do something to try and reveal him as a traitor in order to protect the Kingdom.