Don't know about the twin part but we just went with ours who were 5(just turned 5 about a week prior) and 6. We did the stingray snorkel but we had grandparents with us which made it alittle easier. My husband had one and I had the other. Would be hard if you didn't have help.
We did the Dolphin Encounter in Cozumel. Would be really expensive with your clan but we had a good time, maybe just to Chakannaab without the Dolphin, really neat park with a great beach. If you want to snorkel, they have a snorkeling beach and maybe one of you can take turns taking the kids out. I think the sea lion show looked great, but we missed it. If the 6 year olds are good swimmers, then the Dolphin might be ok, but I would definately reccomend Chakanaab park, I know they offer one with the Sea Lion show or you can do it on your own. If you do it thru Disney, they take care of the cabs and such which makes touring an island with little ones easier.