When I worked at Disney World, one night I was working at a food stand in front of the Castle in the Magic Kingdom. It was between the parade and the fireworks, so there was a huge, endless crowd in front of the stand. In the middle of the rush, I hear a lady shout above everything "Help me, please help me! My daughter is having a seizure!" I turn to where she's approaching from the side, and in her arms I see a little infant, shaking. She said her girl had been strapped in the stroller fast asleep when suddenly she just started to shake. At that point I'd only been working there for a couple of months, and I'd never had to call for emergency services yet. I turned to the other girl working at the stand with me, and she immediately grabbed the radio.
Normally when we have emergencies like that, we go on our radios, call our managers, explain the nature of the emergency, then they call the park paramedics. But as it turns out, the girl working with me knew how to jury-rig the radio to call emergency services directly. So she got them on their way, but in the meantime there was nothing else we could do. There were actually a couple of guests in the line who worked as paramedics, so they knew how to hold the little girl so she could get air and keep track of her vitals. After that, all we could do was wait. The other girl had a good handle on the situation, so she stayed with the mom and I continued helping the guests at the stand. When the paramedics arrived she helped the mother explain what happened. I felt bad for being able to do so little to help, so I gave the mother a water (no charge, of course). I figured after all that crying and nearly having a panic attack she'd be thirsty.
I really don't know what happened after that. The girl had stopped seizing and was stable by the time they arrived, but they still needed to have her checked out. The mom left, the girl I was working with didn't get in trouble for not telling the managers first, and I guess the mom and her daughter are okay now. She should be about three by now, I think.
Either way, definitely a scary and sobering experience. Anyplace is a bad place for your child to have a medical emergency, but I feel like Disney World is a particularly horrible place for it to happen. It would make it a very hard place to go back to, I think.