What have I just read? 
So basically Dad does Mum a “favour” by having his own DD 2 nights a week because it suits her career?
If something happens to Mum, that Dad won’t step up and the DD will go to other family?
He doesn’t currently have a room for his DD so the new arrangement will be an “upgrade”?
Dad’s home isn’t DD’s home?
It was just a drunken one night… so that makes it all okay?
2 year old will just be a visitor in yours and DP new home for the next 16 years or so?
I appreciate you and your DP want to be together, but this doesn’t actually sound like a very healthy set up or environment for this little girl.
To your question about the rooms- well I see your point a bit as it sounds like you will be contributing more overall if you are the higher earner/bringing more into the relationship even if you are putting towards the house 50/50. But I’m not even sure how you would split that? It’s just one of those things in a relationship I think, if you live together it’s never going to be exactly fair. Difficult when there are children involved too.
When I lived with my ex DP, he had one of the rooms for all his sports memorabilia etc. technically I guess I only had half a room as we obviously shared a bedroom. I still paid 50/50 towards everything- maybe it wasn’t fair but never crossed my mind really.