No one will try to stop you if you bring your kids in, but be prepared for people not to like you very much, either. I've seen the cast ask parents things like, "So, do you always bring your kids to bars?".
Also, the performers will tone down the show if there are children present- it's not very dirty, but there can be a lot of innuendo and it can get slightly racy. Adult patrons without kids can get resentful about that- I don't think anyone (sober) would say anything to you, but I've seen parents who brought in kids get some mighty dirty looks in there.
If you choose to bring the kids, do it early before the drinking really gets into full swing. It's fun, but it is a bar, the drinks are strong there, and frankly, part of the act is that patrons are encouraged to drink heartily-there are plenty of jokes about alcohol and the club salute/official drink is the Kungaloosh, for example.
If you don't want to expose your kids to a bunch of loud, rowdy, cheering, singing-along-drunks, maybe the AC after, oh, 9 PM is not the place to bring your children.