There are signs at the CR that state that they are unable to provide parking for the theme parks.
Valet parking might be an option, but, if it's a holiday or there's a large convention, they might not allow you to utilize that service, just be prepared in that case.
We've always been given a three hour parking permit. Sometimes they've had a list of ADR's, sometimes they haven't.
I have seen cars towed out of that lot while watching the marathoners run past from my balcony. I watched the tow truck circle following a Disney security vehicle. The Disney security guy would hop out every now and then and check a permit in a windsheild. Twice he motioned to the tow driver to remove the car. While I don't think it happens every day, it does happen. The lot wasn't all that full that day, so I was surprised that they were towing cars.
The easiest way to make sure that you'll be able to park and get to your ADR and not have to move the car afterwards is to park at the TTC, take the monorail to the CR, then walk to the MK after breakfast.
Have a great trip!