sounds like a lot of splitting of hairs here...putting that aside.
the Yucatan peninsula is the part of Mexico that is a large limestone shelf that sticks out from the mainland of southern Mexico like a big toe. I contains several Mexican states including Yucatan, Quantana Roo and Campeche. Most Yucatan residence almost think of the Peninsula as it's own country and not really part of Mexico proper from what I've observed and read. I also seems from what I've noticed that the people of the upper Mexican states sort of feel the same way, it may go back to the days of the Maya where there territory was the Yucatan and upper Central America and other than for trading reasons were seperated from the rest of Mexico.
Cozumel Island may or may not be technically "in" the Caribbean Sea as the leaward side of the island, the side that faces the mainland has the Cozumel Channel as a body of water and the Caribbean Sea doesn't really start until you get to the most southern and northern parts of the island. Although I'm sure some will argue that the Cozumel Channel is part of the Caribbean Sea, if you look at a really good map, they are listed as seperate bodies of water.
Again, this is just really splitting hairs, the simple answer is that Cozumel is part of Mexico and that is why it is on the Mexico board not the Caribbean Board and the reason the Bahamas are on the Caribbean board is probably because although technically they are there own island chain and in the Atlantic Ocean and not part of the Caribbean, most people think of them as being Caribbean and also most likley for web space simplicity reasons, it probably wouldn't make a lot of sence to just put the Bahamas, Turks and Caicos on their own web page.