You will be charged one night for the car parked in the resort parking lot. You can move that car in and out of the resort as you wish. If you move your car to the Citywalk (park) parking garage, you will have to pay separately to park in that garage unless you have an AP with free parking privileges.
However, there is no reason to move the car to the Citywalk (park) parking garage. This would be a longer more crowded option for going to the parks, especially on a HHN. Also, the security lines are worse in the parking garage. Although, overall security lines aren’t too bad at Uni.
Don’t think Disney transportation where you might want your car in the park’s lot. There’s just no advantage to it at Uni. The hotels are right beside the parks and only a very short walk away. If walking sounds too tiring, there are also boats. The walk to the parking garage will end up being just as long and there’s no boat option for that.