As the mom of 3, I have a problem with the old "do as I say, not as I do" approach to parenting.
I think I would make alternate plans for my kids for that day so they were unable to attend the party. Build a bear, amusement park-- some way they could have fun without breaking the law.
In our neighborhood, people who live in "Levit" (as in Bill Levit) houses support the local town pool through their taxes. People who don't live in Levits don't support the pool and don't have access. The problem is that, with the exception of about 2 blocks worth of houses, EVERYONE in my kids' school lives in a Levit. And you guessed it: we're on one of those two blocks.
Lots of my neighbors get around it-- they "find" pool passes or have friends lose one and replace it. But that's not the type of parents we choose to be. We have a backyard pool and the kids are free to invite any and all friends. But I refuse to teach my kids that it's OK to break the rules that they don't like or that aren't convenient to them.
OP-- good luck with this.