DH and I went to Cozumel without the kids last year and stayed in a resort on the island.
We promised to wait to do the dolphin excursion until our kids were with us.
Our hotel overlooked the Dolphinaris, so we observed from above.
It looked like the Dolphins at Dolphinaris were in pools. I don't know what else they had there to do, because we didn't go there.
We went to chankanaab park for the day and snorkeled.
This Sept I think will book Chankanaab for our family to swim with the Dolphins.
At Chankanaab, you are in the ocean with the Dolphins, but it is a fenced in area so nothing else can get in/dolphins can't get out.
It looked like you stand on a platform in the water and take turns meeting/swimming with the dolphins.
Also at the park is a nice reef to snorkel and a beach.
If you look on Tripadvisor, they have reviews and pics of both places,
I think either one will be great!