There are stingrays in a pen at Blue Lagoon. Disney sells the excursion for $60 I think. There is only one way to get to the island other than Disney and that's through the company that owns the island. I've seen postings that this costs $27 and you leave from Paradise island near the bridge, so I'll cost an additional $8 to get a cab out to there roundtrip. Then you probably have to pay $25 or so to swim with the rays - so it will probably cost the same. (Disney might include lunch also).
I swam with these stingrays 4 years ago. The water in the pen area varies from 10 to 4 feet deep. When you first go into the water, the stingrays immediately come up to you because they have learned that new snorkelers might have food. I was immediately greeted by 12 big stingrays before I was even half in the water and it was a little scary. Part of what made it so scary was that there was some guy who wanted to get his picture with a ray so he had his wife stand on the dock with a non-waterproof camera. He would swim down and grab a ray and wrestle it to the surface and pull it out of the water. These critters may be somewhat tame, but it didn't look like the rays liked this treatment and I was worried that they might get angry and they might sting me even though I wasn't the one being cruel to them.
We are going back there in April, but I would be afraid to take my kids (DD11, DS 6) into the pen. Your kids might be braver. I have snorkeled in Key Largo and Cozumel when wild rays would swim by me and it was not nearly as intimidating as it was in this setting.
They do have vests for adults but I don't know about ones for kids.