As a dog owner (Golden Retriever) I know how it is to have to put up with people who are afraid of dogs or even uncertrain around them. The fact is, if there are frail old ladies at your house and they fall over because the dog scared them, you are still liable, even though you did nothing wrong. Welcome to 21st Century America and our fine legal system. for your sake, I hope the dogs are in the garage. It's not worth the worst case scenario.
I'm afraid of dogs, have been even before the abuse. I remember being scared of my best friends dog when I was in 1st-4th grade. She was a big St. Bernard named Lizzy. We just played in the walk out basement, I think I only saw his room once. Its probably just a childhood fear that I never grew out of because of the abuse. I don't remember being bit by a dog or anything.
I'm not too social so I haven't had to deal with this but I think that if I had a friend who had a dog. I'd talk with him but if he didn't feel right about it, I would just have him over my house or go out or something. To be honest, I guess I probably should get over my fear of dogs, but right now with the abuse I have enough to deal with.
As far as Mom planning a BBQ at your house, yep, she stepped over that line. If she wants to have a BBQ and her house isn't big enough the she should ask you. If you say no, thats up to you but she has to ask. I venture if you decieded you wanted to plan something at her house without asking she'd be pissed.