My DM is hoping online opinion will make this not a broken heap. 

Pact of the Glove

Your patron gives you a glove or pair of gloves or similar hand covering. The glove is treated as a spellcasting focus for your warlock spells.

You learn the Chill Touch and Mage Hand cantrips. These don't count against your number of cantrips known. Both spells appear as spectral versions of the glove granted by your patron.

When you cast Mage Hand, you can perform the following additional tasks with it:

      • You can push or pull one willing creature, Medium        size or smaller, 5 feet in any direction.

• You can use the Help action, but only to aid in skill checks using the targets hands (Sleight of Hand, Tools et al, GMs discretion), and in combat only if the enemy is within 5 feet of the target, and you can see both of them.

Additionally, when you hit a target with Chill Touch, their movement is reduced by 10 feet until the start of your next turn.

(Destructions/loss of glove rules should probably be the same as Book of Shadows for PotTome?)

There’s that then. Now, invocations so this is worth something

These Hands

Prerequisite: Mage Hand cantrip

• When you cast Mage Hand, a number of hands equal to your Charisma modifier, minimum 2, appear. The hands can carry up to 15lbs * your Charisma modifier.

Spectre Boxing

Prerequisite: Pact of the Glove

• When you take the Attack action, you can make one of your attacks with Mage Hand. This is a spell attack that deals 1d4+half your Warlock level (rounded up) bludgeoning damage.
• This damage die increases at 5th(1d6), 11th(1d8) and 17th(1d10) level

Grave Grip

Prerequisite: Pact of the Glove

• When you hit with Chill Touch, you may choose to reduce the damage by 1d10 to reduce the targets’ speed by half instead of 10 feet, if the creature is Large or smaller.
• At 5th level, you can reduce the damage by 2d10, and the targets’ speed is reduced to 0 instead.

Swarm of Palms

Prerequisites: 5th Level, Pact of the Glove, These Hands invocation

• When you cast Mage Hand, you may choose to concentrate on the spell; the duration is unchanged. While concentrating, the spells’ range becomes self. Your space becomes lightly obscured, giving you half cover, and spaces within your reach become difficult terrain for the duration. Creatures bigger than Large ignore the difficult terrain. The spell ends as normal if your concentration is interrupted.
• You may also cast Mage Hand in this way as a reaction if a hostile creature enters your reach. You must concentrate on the spell when casting using your reaction.

Master’s’ Hands

Prerequisites: 7th Level, Pact of the Glove, Spectre Boxing invocation

• When you use the Attack action, you may cast Chill Touch as a second attack. It’s range becomes 60 feet if you cast it this way.
• You add your Charisma modifier to damage rolls for Chill Touch, and Mage Hand when using the Spectre Boxing invocation.

I don’t see much point in building past here if this is DOA. If this seems potentially workable,  maybe later on you carry more with Mage Hand, or even get a climb speed while using Swarm of Palms? I started with Bigby’s Hand as an answer to making Mage Hand as playable as Eldritch Blast as your default cantrip. Help me out, will this suck?

this isn't that bad, but it runs the risk of making pact of the tome seem even weaker and less played. the invocation names may need to be more serious. I like how the mage hand push-pull could be used creatively

For the initial pact feature I would get rid of the slowing effect on Chill Touch. For a Warlock, just getting the two additional Cantrips is a nice boost all on it’s own. 

For Specter Boxing you might want to switch it to Force Damage and maybe just scale back on the damage a little, 1d6 and then just have it scale the same way Cantrips do? I personally love that you went a different way with it, but an automatic 11-20 damage at higher levels might be too much. Only playtesting will tell. 

For Grave Grip, I would bring that awesome idea to use chill touch for slow here. It would fit more in line with the invocation that does it for Eldritch Blast. Just dropping them by half is a good feature.

For Swarm of Palms you referenced “Your space becomes lightly obscured, giving you half cover, and spaces within your reach become difficult terrain for the duration.” I assume that you mean the “space” on the grid, but a lot of people don’t play on a grid, so you might want to change that to “You count as being in half cover, and the ground within 5-feet of your counts as difficult terrain” or something like that. 

For Master’s Hands I would change “you may cast Chill Touch as a second attack“ to “you may cast Chill Touch as a bonus action”

Maybe another Invocation to Bigby’s Hand once/day?