I'm normally the biggest proponent of listening to your instincts, but in this case I think they might be misleading you.
I think your gut feeling that she doesn't like you is HEAVILY influenced by your knowledge of the situation - i.e. because you know about the relationship and they don't, you feel like everyone must be able to see it really easily and therefore they're all going to disapprove and it's all going to go wrong.
And given that his mum doesn't know the situation, it's likely that even if she DOESN'T like you, it's nothing to do with your relationship to her son. Not everyone in this world is going to like you, but according to your post she was at least cordial. That's good - being able to deal with people you don't personally like because someone you do like likes them is healthy behaviour.
As for the goodbyes, I think you're reading too much into it. Not only might she know some people better than you, but even when I say goodbye to my family I don't necessarily give the exact same of interaction to every person, and it's crazy to expect that everyone gets an exactly equal goodbye.
Given that her mum was at least polite, and the rest of her family seemed to like you, I'd say that you made a good enough impression.
I also totally disagree with the idea that she's confused as to why you're bringing "a friend" for Christmas - I've had loads of friends to family meals and stuff. I'm the sort of person who doesn't like seeing people left out, so if someone's got nothing to do, then I'll invite them to spend the time with me and my family, so at least they're not alone. Isn't that what Christmas is about anyway?
So, essentially, I think you should just go to the breakfast. If the mum is the one organising it, perhaps buy her a small gift (separate to your bf/his gf) to say thanks for the invite. You're not trying to buy her affection mind, so don't make it too big/expensive, it's a small token to say thanks for someone inviting you into their home (and hopefully making some yummy food for you