I don't think sending it is wrong - they might like to see it if nothing else (although do the birth announcement as well, of course). And they would probably like to feel included in that way.
I've got family a few hours away, but I'm just planning to send out Facebook messages informing them "If they happen to be in town" that weekend. My bff is doing the shower and I don't want her to have to pay for postage for people that are almost certainly not going to be able to make it :).
That being said - my situation is extended family, not my mom, so I would absolutely send her one, even knowing she couldn't make it!