If you are divers the Eastern coast is great. The surf is too rough there for good snorkeling.
For children I would use caution as the surf is very strong on that side and there is severe undertow in some areas...swim there with caution...
There are a few good snorkeling spots on the Western coast, but unfortunately they are in front of either Chankanaab Park (a National Park with a great snorkeling area, a separate cove for swimming, a dolphin encounter, etc. The area near the Presidente Intercontinental hotel has wonderful snorkeling but I'm not sure how you can access it without being a hotel guest.
The cozumelinsider.com website has more info on Cozumel beaches and which are best for what interests you.
Your idea sounds idyllic though and I hope you find someone to take you there!
Just as a side note, if your Western Caribbean cruise happens to take you also to Grand Cayman, you could come closer to this experience there I think if you hired Captain Morgan to take you to Cayman Kai on the North Point of the island.
Happy sailing!