I used an offsite shuttle last year from a Marriott property - and don't ever want to do it again! It ran 3 times per day to Epcot - 8am, 9am & 10:30am, then returned from Epcot at 5pm, 6pm or 10:45pm. It was first come, first served & you had to sign up in the lobby the night before taking the shuttle. The early shuttles were full immediately, so if you were in the parks & not there right at sign up (5pm I think) you missed out. I was solo - so it worked fine for me, but there's no way I'd want to have to rely on it with the kids. It was a shared bus between 4 other hotels, so it was a LONG ride (almost an hour) and over-full at all times. It only dropped off & picked up at Epcot - and waiting in the offsite bus pick-up at 10:30pm wasn't a fun thing to be doing. That area is WAY out past the Disney transportation, and the taxis, on the far side of the Epcot parking lot. I can't see doing that with kids, having to ride an hour to Epcot, then transfer to a bus for another park, and then vice versa at the end of a long day.
Just my experience, I'm sure some other hotels have much better shuttle service!