Birthday party invites and siblings

I need some advice. My five year old is getting invited to a lot of birthday parties this year. I always leave my three year old at home, as they weren’t invited.

This week, my five year old got invited a bounce play place. The family said they rented out the entire place and it’s a joint party for two of their young kids. We’ve been there before and my three year old loves it.

Is it ridiculously rude for me to reach out to the mom to ask if I can bring my three year old? I was thinking I could offer to pay for her separately but I know this will put the mom on the spot and not sure if I should.