But if it were common in a family for members to all stay at each others houses, and one branch of the family doesn't do that and doesnt explain why, the rest of the family might be confused and the OP might come across as standoffish. Then, when OP doesn't show up to several events at a wedding, the first assumption would probably be "Oh, well its probably the same reason they won't stay with us when they are in town, they just like to keep to themselves." Not, "Maybe they didn't get the invitation."
I can definitely see this happening. I also don't think it's particularly rude for family (or even very close friends) to invite themselves over for visits, though. It'll depend on the family culture, of course, but if I were visiting a town where a family member lived I wouldn't find it at all strange to ask to stay with them. Assuming I can stay or insisting on staying regardless of their feelings or plans would be rude, but asking seems fine. That's very common in my family as well as the families of most of my friends. If that's not something OP is comfortable with, that's of course fine, but OP should maybe explain that so as to avoid misunderstandings.
Inviting oneself along to a planned event is a different matter, though again if it seemed like everyone in my "category" (level of closeness to the host, group of friends, etc.) were invited and I seemed like the odd one out, I would do a little investigation. Which, as other posters have said, could easily take the form of, "What dinner? I hadn't heard anything." There are many situations in which that kind of inquiry would be awkward, but in the case where it really doesn't make much sense for you to not be invited, it's warranted IMO.
Right now OP seems to be in the position of rebelling against a larger family culture on principle, which I personally don't quite understand. I see etiquette as more of a general standard - something people can lean on to prevent misunderstandings and guide conduct. It makes sense for that to relax when around people who are close enough not to "need" it as much.