No babies allowed at wedding

So my cousin is getting married this September and my family is going. I live in Chicago and the wedding is in New York. I've already taken time off of work, arranged a hotel for us, and everything has been paid for. Looking over their wedding website, I noticed they said "ages 13+ only. Now, my daughter will be 8 months old when we go, and everyone in New York is excited to meet her, so I figured that age rule didn't apply to family. Asked my cousin anyways and she said strictly no children under 13, but they're going to hire an on-site certified babysitter for all kids. A couple of problems I have with that...

1. I don't know this person, I didn't run their background.

2. My cousin has 2 sons under 13, one of which is severely autistic. I last saw him when he was 1 so im not sure how severe it is other than he is nonverbal. Will I have to worry about him having a meltdown with the babysitter and having my daughter there?

Am I over reacting to this? Not quite sure how to handle this lovely situation...