Agree with Rach on this.I understand why you're pissed off but his older daughter is still his daughter,and you don't actually get to choose when you give birth.This is also the most important day in her life too.So he does have the right to be excited about his Grandchild,and obviously wants to meet him and see his daughter.
However,he also has two other daughters and when you're three your birthday is your own very special day,and Mia shouldn't have to fight for her Daddy's attention that day.
I think probably your partner is torn between his children.However if his older daughter is old enough to have a baby,is it not time for her to behave like an adult now,rather than attention seeking like a spoilt child.Your partner's Grandchild will always be a part of your family's life,like it or not cos they're your husband's family.It's up to you what part that is,but it's really down to your partner to deal with his older daughter.It's not a problem that will go away.It'll come up every birthday,and he needs to be fair to everyone,and whatever stunt she pulls to upset your relationship,he needs to support you too.
Hope you had a lovely day anyway