You must stay onsite - there are benefits such as Disney transportation and possibly some Extra Magic Hours, depending on what you want to do - but timesavers. I would say that with only one day that you will not have time to park hop and park hopping adds a lot of $ to the admission price. Especially since Disney has a structured system where the price per day drops for every day that you add. Only going for one day and adding the park hopping feature will make it really expensive. The other thing is that your one day really isn't one full day since you'll be coming from the port, checking in at your hotel...I would guess the morning could slip away from you and it could be 10-11:00 before you actually get to a park. I don't know what the park hours are in the fall, but I would guess things might shut down a little earlier - you might find MK open until 11:00 tho.
Somebody else mentioned food...I would say if you had more than this one day to definitely plan a nice dinner somewhere...but again, with only one day I would not try to tie myself to a time for dinner. I would just wing it and play it by ear and eat CS somewhere. My family HATES it when I am pushing them to be somewhere at a certain time. In July we only had 2 1/2 days. We flew down early but by the time we dumped our stuff in our room & started out it was probably close to 1:30. We had dinner ressies at Mama Melrose at 5:10 for the Fantasmic package so we went to Hollywood Studios...first grabbed a quick light lunch and then went straight to the new Toy Story ride. Fast passes were gone already so we went & got fast passes for Rock N Roller Coaster and then got in the Toy Story line which was supposed to be a 70 min. wait. AFTER we got in line a couple of those Brazillian tour groups came with their fast passes and gunked up the line...we ended up being in that line for 2 hours!!
Then we went & rode the coaster but by then it was almost time for dinner! We didn't have time to make the Raiders of the Lost Arc show or anything. It was a horrible, horrible afternoon. We grabbed fast passes for Tower of Terror before dinner but we just weren't able to accomplish what we wanted to do and spent a lot of time crossing the park. We ate dinner, we rode Tower of Terror and we did something else (I forget) but we had to go to Fantasmic at like 8:15...it just didn't go well. We have been down enough times that we know what we want to ride and we know how to work the system pretty good. But sometimes the best laid plans don't work. This was not our most efficient day ever - so I would caution about thinking you have time to park hop. (PS) I don't think any of the rides at MK are spinning rides except the teacups...tummy's should all be fine!
IMO I think one day is not enough and you should just do one park - probably MK so they can hit the highlights - which for us are Space Mountain (which they will probably want to ride more than once), Splash Mountain, Big Thunder Mountain Railroad, Pirates of the Caribbean and the Haunted Mansion. Beyond that there is Lilo & Stitch, Buzz Lightyear Space Ranger Spin, the Indy cars, Swiss Family Robinson Treehouse, Jungle Cruise...Country Bears...Hall of Presidents...there's some classics too...It's a Small World....Peter Pan....Snow White....the tea cups...we've sort of outgrown some of those but if they've never, ever been they're sort of nostalgic if the lines aren't too bad...we only do some of those if we're done with everything else. If your kids were younger then of course that would be where you would probably start.