I'm going to ask my extended family to not bring their kids to my birthday. You think that's a rude request?
That depends, can you tell me the reasons why you made this decision?
I can't handle annoying children at the table. I want the party to be adults only.
Fair enough, I totally understand your request.
I've wanted to ask for a while, but it seems inconsiderate because my family can't afford babysitters.
Despite the unfortunate babysitter issues, you have every right to not want children at your party.