We sail a Catalina 30 wing keel on Barnegat Bay. From your post I'd guess that last season you were sailing on Little Egg Bay or somewhere south of Barnegat Bay. We started out down there and the difference is depth is significant.
First if you sail in the bay you WILL bump bottom no matter what you sail and TowBoat US is a good idea. The good news it's a soft sand bottom and so far we've had no problem getting off on those rare occasions we've found an uncharted sand bar. A lot of people make it sound like grounding with a wing is the end of the world. It's not, at least in soft sand.
With kids Barnegat Bay offers more options for swimming and dock and dine stops. Tides on the Delaware are 6 to 8 feet with very strong currents. Not the place for kids to jump in the water. We've looked hard at the Chesapeake more than once. For us it's about an hour to the Barnegat from home (near the Betsy Ross bridge). It's two and a half hours to the northern marinas on the Chesapeake. That's a big deal if you're driving it every weekend.
As for wing keels going to windward you'll never notice the difference cruising. The reality is your sailing skills have more effect on your windward performance than your keel; and with a couple of kids on board you and your wife aren't going to be tweaking sails with every puff for maximum speed. BTW, all "shoal draft" Catalina's are wing keels.
You should be able to find a 27-28 in your price range with most of those features. What you will find is that stretching a little on price will get you a LOT more boat. For example check out this Catalina 30
. Assuming it survived the storm it will give you double the living space below deck of a 27 and it will probably sell for around $13-14k. Just something to think about.
Best of luck in your search,