I'm thinking of cancelling our planned vacation because my wife doesn't want to use a car seat for our 3yo daughter
Do you need your wife's permission to cancel the vacation?
It's my vacation. I can cancel it if I want to.
While normally it is good to discuss things with your wife, it is okay in this case since it is dangerous if the child is not in the car seat. It could die if you get in an accident.
Yep, that's why I'm going to cancel.
You're justified in your concern for your child, but canceling the trip seems pretty drastic. Before you cancel the trip, maybe you should try to have a talk with your wife. If you explain to her why your child needs to be in a car seat, maybe the two of you will be able to see eye to eye.