Not familiar with your area, but your most logical first search should be a KOA (Kampgrounds of America). They are designed for young families and usually have all kinds of activities, especially for younger children.
Here's a link to the Connecticut KOA site:
Click here.
And then search out "Private Campgrounds".
But it sounds like what you are really looking for is an amusement park. You might be better off to camp at a State Park that is within driving distance of an amusement park and then just drive into that park for the day.
I don't know of any campground anywhere that has a "Lazy River." But many that is located within close proximity to a water park though. (But, Kansas City-Missouri, Santa Clause-Indiana, Cedar Point-Ohio, Kings Island-Cincinnati Ohio, Disney World-Florida, all might be a little stretch of a drive for you).
__________________
History is not about the past, it's an explanation of the present.
2019 Montana High Country 375FL
2014 Chevy Silverado Duramax, 6.6L Dually