Without reading any other replies...four pages!....my thought is to just leave prior to stripper time.
This really isn't my cup of tea either, even back when I was young and single and childless. It's just not my "thing," and certainly not my "thing" with children and a husband in tow!
Despite the hassle around the transportation of the other kid, I would probably leave anyway and find something to do for an hour, maybe grab some coffee and pie at the local eatery.
Whatever the venue or entertainment that is being offered, you, as a guest, are being told to cover the cost of the party and the entertainment, and this is wrong. Add a little insult to injury, this entertainment is not something you or your husband particularly wish to participate in, let alone the kids. No thank you!
I think I would just say we're going to leave at about 8:45, before the stripper, I hope you all have fun, and leave it at that. If this $10 is a mandatory contribution, skip the party all together. "Thank you for the invitation, we are unable to attend."
I realize there is an inconvenience with the kid and his job, but assuming this kid has had this job for awhile now, it's not a very new inconvenience, but rather normal and expected. It would be nice if you could hang out with your friends/family while you wait at the same time, but it's just not going to work out that way this time. If the host puts pressure on you to pay up, then you need to politely decline, and go about life and transportation as you normally would.