Know the reasons why the relationship didn't work. The thing with having sex is that you have to talk, even if you're trying to be cool or mysterious or leave right after or whatever. You're going to talk and if this happens repeatedly, you're going to bond. In your case, re-bond. Relationships come out of casual arrangements fairly regularly. There's nothing more charming than a naked man in your bed who knows you and knows how to talk to you. I'm assuming a recent ex of three years knows the right things to say. So, if you know this would never work as a relationship, really remind yourself of that. Write it down somewhere you'll see it if you have to, so you don't end up going through the same break up, or in that weird "what are we?" purgatory.
I introduced my girlfriend to my family a few months ago, and my mother hates her. Her reasons (stated or unstated) are superficial, petty things: she doesn't dress well, she makes less money than I do, she didn't go to an Ivy League school like I did. I'm in love with this girl and could see myself with her long-term, but is it worth the fights with the family?
It's really up to you if the pros outweigh the cons, or vice versa. I always try to take the opinions of friends and family very seriously because across the board, they are all smarter than me. Especially when it comes to the people I'm dating because they're not clouded by visions of sex and brunch naps. But reading your question, I do have to say that your mom sounds awful. Are you sure that's what she means? I guess you'd know.
If your mom had something like, "It doesn't seems like she listens when you talk," or "She seems manipulative," or "I think she's a ghost," and then backed those statements up with examples, maybe there would be some validity to what she's saying. But whatever her motives are but it doesn't seem like she's concerned with your feelings. I have friends with significant others that I can't stand. Can't stand their voices, or their dumb stories, or their weird little faces. But I put up with it like a brave little soldier if they make my friend happy. You should see me trying to smile through a conversation about a craft fair or some other nightmare thing that horrible girlfriends always want to talk about.
The point is, your mom hates your girlfriend. Sorry, that's going to make Thanksgiving hard for you. Your mother will eventually come to terms with it, or get tired of complaining about it. It's just not a sustainable behavior. If you want it to stop sooner, call her up, or better yet, take her to the Cheesecake Factory because moms love that place. Tell her that the insults stop or you'll stop being around.
If you have questions about relationship etiquette, please send them to Ask Alison [at] The Atlantic (.com).