No invitation - no gift?

Wife’s cousin is having a destination wedding in Mexico. Her parents got an invitation, as did her siblings, but she didn’t.

We had invited the cousin to our wedding (and she attended) a few years back, her whole family came. No gift given, but she did help bring her grandmother down and we were grateful for that.

Wife seems obligated that she should give a gift to her. She assumes she was passed over on an invitation because we have two kids (5 and 2) and wouldn’t be able to go. Truth is, no, we wouldn’t. I told her it’s about courtesy and thought, her cousin could assume that, but still spend the $3 on an invite and then I would’ve been on board to send a gift.

I boiled it down to my wife that she blew you off, didn’t provide a courtesy, so the same is reflected. You can send a card or call them, but she’s not getting that Cuisinart juicer on my dime. Am I in the wrong for feeling this way?