What we've done is that if our intentions is to pay for everyone, we pay for everyone. That means we may feed people in a different manner or at a cheaper restaurant. It would be rude to say "we'll pay for adults but not kids". Better to just not pay or pay for all.
On the side note, it's perfectly okay for people to assume they will pay but end up asking for just, say, $10 after the dinner and brush off the rest of it or accept what is offered and pay for the rest. This means you have to be prepared to pay all of it though.
In the end, live within your means. Don't have her pay just to make appearances. I know she wants to be nice but no good family member would ever want to put another person off budget knowingly. If I knew my lunch really hurt someone's wallet I would feel awful after and almost mad that I'd be put in that place. Overall, you want this to be an enjoyable experience.
I go out for celebrations and other things with coworkers/family/friends. I've always been prepared to pay my meal even if it appeared to be paid for by the department/family/friend.