I'm a little confused.
You have one cousin who is having a birthday party for her son and his little daycare pals. She never mentioned this party to you nor did she invite you.
You have another cousin who works at the venue where the party will be and SHE invited you.
I don't know your family, but I don't think I'd be comfortable going under those circumstances.
The museum is a public place. No one is stopping you from going there.
I'm assuming the free Santa pictures are a promotion provided for by the museum. Again, no one stopping you from going. But, to show up with your baby and a gift on the same day as the party might be a little awkward since the party was never directly mentioned to you.
I would wait for the invitation to the family party. There will be a million other places to get Santa photos taken of your daughter so it's not like it has to be that day or never.
I would not attend, but that's just my opinion, and again, based on not knowing your family at all.