Perhaps the OP is getting a bit upset because it seems a lot of people haven't read through ALL of the replies?

Based on your first, unedited post, I thought you were asking how to tell her the rest of the family weren't invited. I did think that was weird and a bit rude. However, now that you've said that the family hasn't met yours, and you only put her name on the invite, I think it's perfectly reasonable to be upset that she didn't clarify before inviting her family.