Your kids will most likely have less fear then you! Get them good PFDs and let them "have at it!" Smaller cats and some dinghy type boats are easy to right if they have flotation.
Sailboats (keel type) are not stable in the sense of standing on a boat dock. The more sailboats lean over the more they resist "going over" because of weight of the keel or ballast and hull design; "weebels wobble but they don't fall down" Rounded, vee bottom, flare sided boats, canoes, even rocking chairs have what is called Secondary stability.
"Stable" boats like pontoon and catamaran types don't tip but when they do they reach a point where they just go over. (initial stability)
Boats with flat bottoms (skiffs, some power boats) also feel "stable" until they lean or are leaned over to the point of no return.
Most people new or feeling that uneasy feeling we've all had, want that initial stability because it feels safe. Only after practice and learning or pushing the envelope do we learn that when a sailboat leans it's because of it's secondary stability.
Many people never get used to that "boaty feeling" of secondary stability in sailing. Even the famous saying "Never stand up in a canoe" instills that primal fear of "going over"
I owned my boat 2 years before I got used to it's leaning over. (heeling) And I did know (in the back of my mind) that the more she leaned the more she would resist "going over"
good reading here; Stability Explained