Joint Birthday and SO expects me to be Present

My fiancé told me his BM would like a party for their child and expects that we be in attendance or something in those lines. I told him I’m uncomfortable and don’t see why they should be throwing joint birthday parties. He came back to me saying something like she’s insisting we should have the party and went as far as saying she says things like does this mean we won’t go to school events as well etc. I don’t see how these people don’t see how awkward this can get. I lowkey can’t wait until she finds a partner and then he’ll see how quickly adjustments in these situations will be made to avoid awkwardness in her new relationship. Also, I find it quite annoying that it’s always about the child and never taking into consideration how the partner will feel. Even typing this feels wrong but the reality is even in relationships where the children are from the same mother and father it’s not always about the needs of the children. It’s always a balancing act between the two. I’m also starting to feel like I’m being sidelined but when it’s convenient for him he’ll want me to take on the “mum” role. I think I’d like for us to have a conversation over boundaries in relation to this sort of situation or just how to make adjustments to make me comfortable because this is starting to eat me up. I don’t even know if this makes sense but it would just feel good to be heard by people who understand where I am. Any advice is welcome.

EDIT: Thank you everyone for your input. After much thought and consideration, I’ve decided I don’t mind whether they do joint parties or not. I’ll let my partner and his BM decide whatever they think is best for their child and I’ll support from a reasonable distance whenever necessary. I’ll also do whatever I need to do to protect my mental peace. Let them decide what’s best for their child.