I don't have any grand solution to the larger problems here. Mostly because it's not really your problem to work out - your fiance needs to work it out with his gf. But in the interest of your sleep (and continued sanity) I would seriously consider having him sleep elsewhere for the time being. It is your space and you have a right to invite who you want into it. If his presence is indirectly causing disturbances then kick him out. I'm not sure if there are three bedrooms? It sounds like not. So it may force him to deal with the situation.
Good luck with it, whatever you decide to do.