The thing is, with children that small, you cannot get any peace and quiet in your own home, no matter how hard you try. Locking yourself in a bedroom to watch tv or read a book usually ends up with a little knock on the door and a small voice demanding to know what you are doing or can they come in - it's natural for small children, but it's annoying when they're not yours, and you just want to chill! They want your attention, to play, to be taken to the toilet, to get snacks, to put Peppa Pig on for them etc etc - it's relentless. IME, if you're at home, you're fair game, even if daddy does his best to entertain them. Often the only thing you can do to get some P&Q is take yourself out of the house.
I have been a SM to a toddler, and it is HARD (and you have two!) - you feel like your home and your time is not your own when they are there, so I strongly suspect that's why your gf is out a lot of the time.
I didn't used to hate mine coming over, or have a problem with them being at the house, I just used to prefer the weekends when they weren't - so when your girlfriend says she doesn't have a problem with it, she most likely doesn't - she just has other things she'd prefer to do, and she's just getting on with her life.
She really doesn't sound like she's doing much wrong tbh - she's leaving you to spend time with your daughters, she's nice to them when she sees them. It seems like a mismatch of expectations as others have said - you see her as part of your family with your daughters, she sees herself as your girlfriend. Only you can decide really whether this will work for you long term - it sounds like she doesn't want to give any more right now, and that's her prerogative, you can't make her play happy families.
And as for sleeping on the floor - just stop it. Yes, as their parent you do have a responsibility to make sure they don't wake her up at 6am screaming and shouting and jumping on her, but any more than that, no. Get up with them when they wake, leave your girlfriend in bed, and play quiet games with them / watch tv etc until a reasonable hour.