If you visit a park in the morning (say Epcot), go back to the hotel in the afternoon and then return to a different park in the evening (say MK), do you have to pay for car parking twice ?
If you're staying on-site parking is free at the theme parks.
If you're not staying on-site and pay for parking, you only pay once per day, no matter how many parks you hop to. Just keep the parking pass in your windshield.