Sounds like rude to me. But it also sounds like this is typical for her, so don't waste time getting worked up. She is the way she is, just expect it, make your polite response and move on.
I do feel for you. My DH's side of the family is notorious for last minute invites because they don't send them directly to us, they give it to MIL to get to us. Usually it sits at MIL's house waiting for our next visit (seriously, 44 cents, would it kill ya? LOL) But I've accepted that, this is just the way they do it. Just RSVP and move on. After 20+ years it just rolls off my back now. I don't take it personally, I just get on with my day. I nearly fell over when we got a mailed invite for neice's Graduation and Open House this past May, LOL.
The analogy I once heard is that you go sit under a tree with birds in it. They poo on you. You get mad at the birds --- but, you sat under the tree and the birds were just doing what birds do, it wasn't personal against YOU. It's just what they do. Now, you are more than welcome to change your behavior - ie. don't sit under the tree, or in this case, just RSVP and move on with the rest of your day.