To trailer or not?
I sail LIS off the CT shore also. Don''t let the winter storage issue be the determining factor in chosing a keelboat vs. trailersailor. Shop around and you can find places to winter the boat for a small fraction of what the slip costs. I haul out at a different yard than my summer marina, storage is about 1/3 of what I pay for a slip in the summer, including stepping the mast. Added bonus: the winter yard is several miles up the CT river, better protection from nasty coastal storms.
Go with a keelboat. We sail a 28 footer with three kids, also all under 10. It can get "cozy" and I expect it will be downright uncomfortable as they get older, but I''ll cross that bridge when I get to it.
Long Island Sound is great sailing, but I''d be nervous in a light trailerable boat, particularly with kids on board. I like the sense of security that comes with a fixed ballast keel.