MIL and my brith day together

No, you're not in the wrong. A wife and his mother are not the same and it should be that confusing at all tbh. If he wants to celebrate his mom's birthday you're not going to forbid it isn't it, so he should not get offended that youre also expecting basic respect of celebrating yours as his wife and his own unit of family and that you're not happy with this idea of a double birthday.

Not wrong but he also doesn’t have to be in the wrong either. If you and him normally do things for her birthday yearly? Then maybe you can come to a compromise, both of you. That you’ll do a combined birthday dinner with his mom but you also want something of your own on your actual birthday?

Also happy early or late birthday momma, I hope you have a great one and it feels special for you!❤️

I really don't see anything wrong with this. My and my husband's family have 6 birthdays in my birth month- if we all celebrated separately we'd have absolutely no time for anything else. My husband and I will still celebrate my birthday privately, but we'll also have dinner with the whole family to celebrate all of the birthdays that month.