Well, as far as the stone falling out.... you should NEVER have to be afraid of this. If a setting has been done right, this should not be a problem. If you are worried about it, make sure you have the setting checked by the jeweler. I know that for my first marriage, the engagement ring had a guarantee from the jeweler on the setting as long as I had the setting checked by them every 6 months. They did have to fix the setting one time, too. But that ring was gold, and I don't know what the prongs that held the diamond were made of. I know they bent more easily than I would have liked though, so having the guarantee was a good thing.
The ring I have now... my DH ended up getting it from a jeweler we found on the internet because it's a very custom ring that I specifically wanted. The jeweler was very good to work with, though, and I'm really not too worried about it. Besides, the entire setting is platinum, and these prongs aren't budging.
Really, though, it's more likely that you would catch your ring on something in day-to-day wear and bend a prong than it would get dislodged just riding a ride (unless you hit it really hard getting on or off the ride). But I would say there's no more danger losing the stone doing that than any other activity. And if there's a danger losing your stone during daily activities, there's a problem with your setting.
Now, as far as losing the ring itself.... that depends mainly on how you have the ring sized and you wearing habits. Me - I didn't worry about it in the least. The way I have the rings sized, and the way rings fit my fingers, once they are on, even if they are a little loose, they won't fall off. But you know how rings fit you. Do you have a problem with rings slipping off your hands? I don't think the rides are more likely to knock them off than any other activity, but if you sometimes have trouble with them slipping off some, and it concerns you, then you might not want to take them into the parks.
Also, are you someone who takes your rings off every time you wash your hands? If so, I would say you might not want to take them into the parks. Me - I take them off when I shower, but to just wash my hands, I just leave them on, and figure I can clean them at home later. I would rather do that than take a chance I will forget and leave them on the sink, or knock them down the drain, or something like that. And at the parks, you have the added danger that you don't know who's standing next to you at the sinks, and if you take them off and set them down without thinking about it, they could be gone before you realize it. So if taking them off when you wash your hands is a habit for you, I would recommend leaving them at the hotel.
The only time I left mine behind was the morning we did the Dolphin Discovery tour. This wa because we knew ahead of time that we couldn't take ANY jewelry whatsoever backstage with us, and we didn't want to leave our rings in their lockers. We took them off at the hotel and locked them in the safe in our room. Other than that, I wore them the whole time and didn't even think twice about it.
But I do have some rings that fit loosely, and if they fit the way those rings do, I would never have worn them into the parks. I've had those fly off my hands just walking along. They would never have stayed on during a ride.
Bottom line is...put your rings on someplace "safe", where you won't lose the rings. Now - shake your hand and fling it around as hard as you can with your fingers completely open. Do the rings stay on? Do they slip even a little? If they stay on, and don't slip off at all, then I think it's safe to wear them. You should be able to tell how secure they feel.