If you want to snorkel off a beach & not go out to the reefs, here's an idea. When you dock in Belize City, go down about 2 blocks to the Water Taxi place. (Anyone can point the way). Buy a round-trip ticket to Caye Caulker (about $15 for an adult, less for kids). They have schedules posted of when they pick up/leave the caye.
Boat ride lasts about 45 minutes. When you get to Caye Caulker, go to the 'split' (everyone knows where it is so just ask). You can walk or rent bikes -- it's about a mile walk there. There are shallow areas for your kids, sandy beach, & water of varying depths right offshore to snorkel in.
If you go, stop at the bar on the point & order a "Lizard Juice" -- but only AFTER you're done snorkeling for the day!! Bar also serves simple sandwiches & soft drinks.
You can also catch a Water Taxi to San Pedro (Ambergris Caye) which is a larger caye & town but a longer ride.
My son, 7, & I did this for the day & had a BLAST! He built sand castles & played in the shallows while I snorkeled in the Split. I brought up 2 starfish for him to see & a live conch (which we then released of course). I also saw small sting rays & LOTS of angelfish & a couple of gar.