A few weeks ago, we met my sister's fiancee's family. His BIL invited us all to his parents' house tomorrow. Their town does a big parade and his parents throw a big party. I think it sounds fun, and I want us to go, but my mom feels awkward because we weren't invited directly by the hosts.
If I wanted to go, I would go. I think a grown up child inviting you to a family event that is technically hosted by his parents is NBD. I don't send real invites for my kid's bday parties. I just tell a few family members and then let them spread the word to the old folks that don't email or facebook. So, this does not seem strange to me at all.
Sure, go. If it's a big annual party, the guest list is probably pretty fluid. But if your mom is super uncomfortable, ask your sister to confirm with her FI that it's ok for you to go based on his BIL's invitation.