Unfortunately she doesn't owe you anything OP so whilst being upset is understandable, being angry at her isn't. It's not that the lifestyle is different, it is that she's got a better idea of what life in the relationship would be like, and she doesn't like it, it obviously doesn't make her happy. How much you love her has nothing to do with whether or not she feels the same or whether she should reconsider. Relationships often break down once people have lived together and real life sets in.
You were having an affair OP, I'm not surprised the fantasy doesn't live up to the reality. Equally you're seeing someone who's happy to lie to someone they care about and clearly like enough to want to be around, so I would take what she tells you with a pinch of salt either way. It sounds like a convoluted way of her saying she prefers being at home with them, has tried it with you, and still does miss her previous set up, which includes her ex.
I would just end it, it doesn't sound like it's going anywhere and she's been fairly clear about where she wants to be, and that life with you isn't for her. Your set up won't change. Spend time with your daughter and explore dating women when the time is right. Single ones.
This.
You moved someone in with your child after only a year, during much of which she was cheating on her partner.
Not a great parenting decision really.
You played with fire and put your fantasy before your reality, as did she.
It's over, suck it up and next time if you 'fall in love' with someone who is not single, wait for them to leave the relationship before dating. If they feel the same they will leave and do things the right way.
Not keep one foot in each camp, agree to move in with you and your child way way too soon and then realise how foolish they've been.
Sorry OP, time to get real and grow up a bit.