Daughter wants to move in with her mom

that suck, I really feel for you

there are many side to this and all need careful consideration before make a decision

im really not sure what would be best, but kids need routine, rules and structure, especially at that age so having her live with one of you with one routine and one set of rules would me preferred

now, if your place is the best (cleanest, paid of, soon having a paternal figure (you) and a maternal figure (future wife)) you should document this in case it does go to court

look at it like buying a car for her, don't just look at the color but truly consider the pros and cons of each situation

personally (knowing nothing of this at all, but just spitballing here) I think your fiancée will be the deciding factor in her

right now she sees her as someone whom she has to compete with for your time
if you can find a way (if your fiancée can find a way) to change that point of view you have a chance of succeeding in raising her in a happy home between all three of you

but if she doesn't warm up to your fiancée then moving her in with you is almost certain failure, she will see everything your fiancée does as a personal insult from the colour of the couch to the flavor of the coffee creamer



one final thought to consider, inkjunkie said you are going to be the bad guy, no matter what.
so be it, we are talking about your daughter. she doesn't need you to be her friend, shes got a school full of those. she needs you to be a dad and you are the only one who has the privilege and that responsibility.
you have lived 20 more years then she has and that translates into 20 more years of experience and wisdom. sometimes as parents we have to make decision that our children don't understand (my 4 year old often responds to that by yelling: I don't like you anymore)
but in the end there is no one, NO ONE who cares more for that little girl then you do.

use that to make your decision.