I mean I would say that it would make things even more awkward seeing as OP doesn't know the woman at all and suddenly will be sharing a space with her. Personally I'd be weirded out.

I disagree with this, I think it's completely unfair to not introduce your new gf/bf to your kids, much less move them in, especially since they're is an awkward stage. Why would you want that stage while living together and no one can get away from each other? I understand if they're brand new and the parent isn't ready for the introducing step yet, but once it becomes a serious partner, you need to introduce them before taking any more steps. Your kid should be the most important thing in your life, without introducing them you don't know if your new partner gets along or treats your kid right, you don't know if your kid likes your new partner, which is important. I'm sure we've all heard stories of new bf/gfs treating their partner's kid(s) like shit simply because it isn't their kid, "evil step mother." You're risking a lot by not introducing them, and most importantly, you're risking your kid. I'm sorry to say this, but your kid's well-being trumps your happiness with your new partner. My parents aren't together either, and although my dad introduced me to his new gfs sometimes, he also did a lot without telling or asking me. He lives with my grandma and grandpa, and grandma is a sweet lady who can't say no, his one gf had 3 kids. Well he moved her and the 3 kids into the house he shares with them, and later, her best friend, her bf and their 2 kids as well. In this 4 bedroom house, which comes down to 2 because my grandparents sleep separately, there was 8-11 people in it and I'm there on weekends. It was hell, the kids got what used to be my bedroom because there was no other option, and that left me with either the couch, or with my grandma. He did this all without asking or even letting me know. I was a 13-15yr old without any privacy or place to go to get away from these 5 kids that were all under the age of 10 and they were incredibly rowdy. I eventually stopped going over there because I couldn't handle it. You need to consider your own kid when a new partner comes along, they come first.

Like 5 said, that would just make things even more awkward. I'd imagine/hope that they at least talked about his kids, and that the girlfriend at least knows he has kids, but it's still unfair to both parties for the father to not have them meet at some point prior to moving in. What if the kid and girlfriend hate each other? Then the father has to choose between his kid and his girlfriend, and what do you do there?

This is much more than just letting the right person into his home and seeing his family. Rather, he's having his girlfriend move in without telling OP first. Pretty disrespectful of the father. So, it's a little different than your boyfriend and his mother's situation.