I want my mom to cook for me on my birthday
Why do you want to make your mom cook on your birthday?
She loves to cook for me. She does it all the time.
Obviously, you shouldn't force people to do things, even just household chores on your birthday. However, it sounds like cooking for you would make your mom happy, so it's probably a win-win situation.
It's definitely a win for me.
That's good. I hope you enjoy your birthday.