How will you feel if he moves in as a roommate and continues to pursue outside relationships? A roommate would have that right.
I would spend some time thinking about it and writing down the pros and cons from your perspective.
Would you want to establish any conditions before he moves in?
Will he accept your conditions?
What will you do if he violates your conditions?
Don't do it because he wants it, do it because you think it's the best thing for you.
With regard to your daughter, she's going to be happier living with you alone if you're happy, than if your H is there and you are miserable.
Hopeful, I'm just a guy who went through a marriage crisis and did a lot of reading / therapy / research / thinking / etc. That doesn't make me an expert. Definitely solicit some other opinions on this, and if at all possible do a session with a DB telephone coach on this site. This is an important decision, and they can help you with it in the best way possible.
--Accuray
Married 18, Together 20, Now Divorced M: 48, W: 50, D: 18, S: 16, D: 12 Bomb Dropped (EA, D): 7/13/11 Start Reconcile: 8/15/11 Bomb Dropped (EA, D): 5/1/2014 (Divorced) In a New Relationship: 3/2015