Hi there! My husband and I have been to Cozumel and Cayman a few times on cruises. We also spent a couple weeks in Cayman. We've done Chankanaab a couple times, but we preferred Cayman for snorkling. Eden Rock is amazing, but not ideal with kids, you kind of have to swim out a ways, and sometimes the water can be a little rocky. However, I think either Smith's Cove or Cemetary Reef would be great, depending on the ages of your children. If your children are younger. Smith's Cove might be better. It's pretty accessable. You don't have to swim out to get to it.
Also, these places don't get as crowded as Chankanaab.
Hope this helps!
Lisa.