Most Helpful Guy
I wouldn't recommend it. Doesn't matter though; it is your best option. Do it.
A slow transition is the way to gobut before you move in, like everything else in the universe, get a contract for how much rent actually is and something that legally says you are splitting this and that. Why? Because humans are insanely unpredictable. It doesn't just protect you, it protects your daughter, and the fact that location is right next to home is such a plus that I'm not concerned as I would be if it were anywhere else and things do happen to go sour.
I don't think it will mind you but you plan for the worst and hope for the best, esp. if you have children involved, and the simplest way to work with this is to just cover your ass so you can move into forever happy after land.
So the checklist is simple:
1. Get an actual agreement that dictates what you will really pay.
2. Move your stuff slowly so that the transition is easy on the child.
If he resists the contract just tell him that you want to do it for your child ( because you do ) and that since both of you have been screwed in divorces and love in general it isn't so much a matter of trust as it is as matter of learning from your past mistakes. He will respect this far more than if you give an emotional answer since it makes a hell of a lot more sense AND he can relate. It's win/win0