We will be there from November 19th to 22th and looking for a way to organize a private cruise from DRM to Cozumel. Program: Sea, Sex, Sun, Snorkeling and fun! Any recommendations? If you are down, let us know.
LOL - I hope you realize, by private boat it would take you all day just to get from Desire to Cozumel one way - if you could find a boat that would do it for you ... FYI - Diving is great in Cozumel, snorkeling not so much. In fact the best snorkeling in the area is almost directly a mile or so off shore from Desire Rivera Maya
I have seen people booking a private boat at Temptations for the size group you are describing but it isn't going to go to Cozumel. Everything else you want sounds good.
I think what the O/P is thinking about (or maybe "should be" thinking about) is La Isla Mujeres. THAT is do-able. Cozumel... not so much on a day charter.