I personally would have reservations. No communication from either of them (to you) sounds like they don't consider you as having a say.
It may work out fine, but it may not. They are a team, Dad and daughter and they may gang up on you!
Probably the best thing to do is give it say six months, and be clear about that. Set out some ground rules but nothing too extreme either, just the usual things.
As for rent/contribution maybe rather than a set amount, ask her to pay a certain bill every month, electricity, gas, whatever. That might stop her having two hour showers lol.
If you feel your views are not being regarded, then it's time for a rethink. I note you say in a pp that you feel like moving out. Well as the house is owned by both of you, if it gets too much I'd sell it and you can get your own place, and Dad and DD can live together. A pp also said that neither her mother or father want her and how sad that is. I don't see that, DD wants to stay where her friends etc. are, and for all we know she could have gone with her mother.
Anyway, I would hate to be in your position. But at the end of the day, I would look after myself. Happiness doesn't really come from sacrificing yours for others.