So don't go. If she keeps insisting, then you start insisting she must reimburse you for gas and the hotel bill.

So don't. Problem solved.

You don't want to be with your mom on your birthday? It was a pretty big day for her, too, Mister! I always wish my mom a happy Mother's Day when she calls me on my birthday recognizing her role in the event!

It's obviously very important for your mom, I assume she wants you to be part of the family. Especially since you call him her husband and not my step-father. I think that if you don't want to spend time with them you should talk to her, but using your birthday as an excuse sounds immature. After all I assume that it will happen every year, and letting you go once will probably mean that you will avoid them every year. Instead you could support your mom in building her new family relations. And try to be creative like it with them in some special way. Or plan something for the day after.

First, how old are you? Are you a child or a grown ass adult living off your mom? If you're a grown ssd adult, move out on your own. Problem solved.