His moralistic mom thinks they're living in sin
So get out of the hoping-she'll-butt-out business altogether. Life has pointless frustrations enough. Besides, she can be toxic to your relationship only if her son grants her that power, and apparently he hasn't.
Try celebrating that, along with the many things you and your boyfriend can do about his mother: ignore her; trust your own judgment; rejoice in the relative infrequency of her butt-ins (at "once every three months," she's a rank amateur); take her less seriously; take yourselves less seriously; love each other; keep taking each other's side; screen your calls. In order of mounting importance.
I love my girlfriend but I can't stand her relatives. How can I gracefully avoid social gatherings like cookouts without letting them (and her) know that I don't like them?
To avoid letting them know: Decline most but not all invitations. That way you have courtesy cover and aren't making an obvious statement.
To avoid letting your girlfriend know: a very bad idea. Just as her relatives are part of who she is, your dislike of them is part of who you are. She deserves to know whom she's dating. Out with it.
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