RWI's (Recreational Water Infections) are usually caused by swallowing water that has been contaminated by fecal matter. Typically, when they can pinpoint a source, it's linked to swimming in pools, waterparks, bodies of open water. Diarrhea is the most common issue, followed by respiratory infections, skin rashes, ear & eye infections, etc.
At the risk of being gross, one of the reasons people are asked to shower @ DC, or any public pool for that matter, Is to remove any residue of this sort entering the water. Same with swim diapers, please use them parents!
There was a highly publicized case of serious bacterial nature at a WP in the news this summer, but rare to hear IMO. Can't say I've read anything associated with the Orlando parks/resorts, other than random reports of people having skin reactions to likely over-chlorinated pools.
It's my understanding the snorkling water @ DC isn't chlorinated due to being salt water. That said, I'd think it highly likely they still routinely test the quality of the water as to germs. They have $$$$$ invested in the marine life, not to mention wanting to avoid any bad PR as to a rash of park-linked reported illnesses.
OP unless your dr did a culture to determine the specific germ, as you state, you can't really tell where/what you picked up. One of my kids is prone to swimmers ear/inner ear infections due to physiology of his ear canal. If he doesn't take simple, preventative measures, it's almost a guarantee he'll get an ear infection when swimming.
Still, it sure is no fun to get sick on vacation! Hope you're both feeling a bit better now and glad you had a great time at the park.