I would always recommend driving your own car for a dinner reservation. It only takes once standing at a bus stop or boat launch, watching the clock tick and knowing that you are about to miss your dinner at Cinderella's table, to make you leave in plenty of time and have as much control over your situation as possible!!
As far as valet parking at the resorts, I've parked at the Contemporary and the Boardwalk in order to get a meal and asked if I needed to come back in 3 hours and move my car from the valet to the TTC or the main Epcot parking lot. Both times the guy looked at me like I was crazy, and said if I used valet parking they didn't care how long I stayed. I was getting valet parking free anyway as a
DVC member, so I made sure to ask, but they have never made me move my car.
Come to think of it, they didn't make me move my car when I had dinner at Narcoossee's over Spring Break, either. We had dinner and then went to the MK for the evening - I got back to the GF about 11 or so, and the valet guy was happy to get my car - never said a word.