I'd look at either mirrorless cameras (like SLRs in that you can change lenses, but significantly smaller, will have full auto settings, and they're super fast to autofocus, especially the newer models), or a high end compact, ie. Sony RX100, Canon G16, Nikon P7800.
The mirrorless cameras are much smaller than an SLR, but still often bigger than a P&S (except the Panasonic GM1, that thing is tiny!). Most of them offer significantly better image quality than a point and shoot will in a fairly small package, but unless you want to get a bigger lens, your zoom will be limited to about 3x. If you really want something small and don't mind limited zoom, take a look at the Panasonic GM1, you'll be surprised by the size! Other good options are Olympus (E-M10 is a really popular entry level, or the E-PL or E-PM series) and Sony (the NEX-5 series are older, but super popular, the newer model is the A6000).
If even the possibility of switching lenses is not for you, a high end compact works really well for Disney. Gives you better low light performance than most other P&S cameras, but still stays small. Your zoom is still usually limited to around 5x, but I find for Disney that you really don't need more than that. I personally got a Canon G16 for the parks when I don't want to bring my SLR. The best of the best is the Sony RX100 series. The newer ones are slightly faster to autofocus, added Wifi in, tilting screen, etc., but as a PP said the original (if you can find it), is still a great camera! I personally find Sony menu systems a little frustrating, but if you're most shooting auto or scene modes, that probably won't be a problem. The Nikon P7800 is a good camera as well, although not as popular as the Canons for whatever reason. My other recommendation would be the Canon S120 (or a previous model). Very small camera, doesn't have as good of a lens as the G16, but is much smaller, and if you're mostly shooting in auto you won't miss anything else that the G16 has. My friend has one and really likes it.
If you like doing your own research and comparison, check out Digital Photography Review's website (just google that). They're an independent reviewer, and should have reviews up for all the cameras everyone has mentioned. My other suggestion would be to go to a camera store, and try them out! Some will just feel better in your hands, and be more intuitive. If you haven't guessed by now, I work in a camera store, so if you have any little nitpicky detailed questions about any of the cameras out there, I'd be more than happy to see if I can find an answer for you. Happy camera hunting!
