I really wish some people would actually read the posted question before responding.
Frometoz's COUSIN said that Frometoz didn't need to be updated.
Frometoz's COUSIN said that Frometoz didn't care enough to send a gift to the baby shower.
Frometoz was NOT invited to the shower.
Now that I've said that...
If you are not invited to a shower (baby OR wedding) there should be no expectation that you will send a gift.
Some people feel very entitled to whatever they want because they were never told "NO" as a child... she sounds very much like that.
I would go ahead and send a gift to her house like you had planned. Her greedy, petty attitude does not warrant any special treatment, but try to remember that the gift is for the baby. Not the crazy mama.