LW wants to use Nora to f-you her parents. That's a big no.

She could invite Nora and her sons as honored guests and seat them with people who they will enjoy meeting and talking to, if she has any such people at the wedding. Honestly, though, someone one talks to just once a year at the holidays is waaaay below my cutoff for wedding invitations. (Isn't she sending Nora a birthday card and flowers? Is it really just only once a year? Then they are not close.)