Oh I don't know Troubledsister, if I would bother asking your parents. If you ask them not to mention to AB about coming to your house, you make it into an issue. And if it becomes an issue, your AB, if he finds out about it, may be so pissed off that he may just stop by anyway just get your goat. Which would completely defeat the purpose of your request. I'm convinced that my cousin, who is a pot-smoking psychopath, showed up to my aunt's funeral completely stoned and disheveled because he found out that nobody wanted him to show up in the first place.
My sister and I aren't on the best of terms either. The last time we saw each other a couple weeks ago I tried a new tactic which seemed to work very well. I put myself in the role of a journalist and just listened and observed to what she said. I didn't really say that much at all. Making the conscious decision to turn myself into a neutral third party made things so much better. And the vibe between my sister and I was a lot less confrontational than it was in the past. We'll see if this holds.
I really don't expect much out of my sister now. When she's nasty, it still hurts, but I can't say that I'm surprised. I now know that when she's nice, it's usually because she wants me to get close enough again so she can strike within range. It will take a long time, YEARS, for her to prove to me that I can trust her again. A nice word or two just isn't going to cut it anymore.
My parents used to be like your parents. And then my mother got cancer and my sister left my father to his own devices. She kept on blapping on about juice, marijuana, and The Secret as the ultimate cure, and was so judgmental and miserable about my mom's course of treatment that when my mom actually got better neither I nor my parents ever bothered to tell her. The kicker: when she did find out, she kept on saying, "You see, I was right!" Her behavior completely broke my parents' fantasy that she was still functional.