Hi Gina, welcome to the Board. This is a world wide group of divers, but there is organization to the madness. At the top of each page click on the "Forums" button and watch a long list of topics opens up. . . scroll way down this list until you find "Regional Travel and Dive Clubs". Open this group of travel messages and go to "Mexico" There are recent post there about dive shops in the hotels vs. dive shops in Playa del Carmen. . . Price and smaller groups of divers per boat seem to favor the small independent shops, and several shops are recommended by name.
Staying on the mainland, you'll have to cross to Cozumel by ferry, and most dive shops on the island, are leaving on the morning dives before 9 am. Some of the shops in Playa del Carmen can make arrangements for a later starting dive with a Cozumel dive operation.
Also, read the Cozumel board for description of dives, and the many, many dive operations, with almost every operator excellent. Diving in the underwater Park is excellent because of the local guides protecting this park. The guides are diving every day and can almost introduce you to every fish. The guides all speak English, and will customize their dive for little or a lot of attention to fit your experience.