Captain Jacks is not in PI. It's just outside of it.
Be aware that PI is like a big street party with alcohol being servied right in the streets, including shooters. There are a few carnival type games, and usually a live band on the west end stage, but it's not really a "family" atmosphere. It's basically a big outdoors bar, suggestive dancing, drunks and occasional fist fights included.
If you are comfortable taking your kids to that type of atmosphere, you are allowed to do so, however it seems that the majority feel that it's not appropriate for kids. And many adults would prefer to not have kids there, so you'll probably get a lot of dirty looks.
Without actually going into the clubs, which requires admission with no reduced price for kids, and they aren't even allowed in several of the clubs, there's really nto all that much to do.
IMHO the Boardwalk is a much more family friendly/oriented place.
Anne