Normally, third showers aren't appropriate. But isn't there some caveat about when the mother's moved to a new place (or has many years between this child and the one previous?)
If I got your (the OP's) invite, I would definitely accept, whether or not it's etiquettely correct- as long as I liked the new mom and considered her a friend, regardless of what you called it. But I tend to accept any shower invite as long as I like the honoree (or hubby likes the other half), because there are some times I feel friendship transcends etiquette. If there was a new mom in the community and I'd met her and quite liked her, I'd go.
If I was the mom, however, I'd kind of feel awkward. All these people that don't really know me being asked to bring a gift? That would make me feel a little wierd. I know I felt wierd at my shower for my first where some women in the neighborhood were invited, and they aren't people I talk to much at all. (Totally sweet of them to come, but really- a "congrats!" shouted as we take the baby on a walk was all I expected!) I'd prefer a lunch or brunch or whatever you want to call it, just because I'd feel awkward otherwise.
Just my two cents