Let's start with Arcane Trickster. Not bad implementation. Spellcasting Rogue, basically. Aside from the things missing which I mentioned previously, mainly Expertise, there's not much here that is really different...
Except for Mage Hand. It should be invisible, able to be moved via your Cunning Action Bonus Action, able to pick locks or disarm traps using your proficiency (so Expertise would really shine here), and able to essentially pick pockets with Sleight of Hand roll.
It is what really sets the Arcane Trickster apart at lower levels, and mage hand really doesn't function well. It is a lame spell that can't even pull levers. The whole point of it is to manipulate objects from 30 feet away, and I've only ever used it as a diversion for enemies who love to attack it. Not good, especially for the Arcane Trickster.
That said, not much else to say here. Rogue Mage cross class is essentially what this is. Is it special. Sure. It's fine. Other than Mage Hand and no Expertise, they've implemented it fairly well.