Typically if you book a restaurant at a resort, you can park at the resort for free for up to three hours. So, you really have two choices if you are going to MK that day:
(1) You can park at the contemporary for breakfast, and then one person can move the car over to the MK parking lot while the rest go to the park.
OR
(2) Park at the MK parking lot and take the monorail to the Contemporary.(4 stops from the TTC)
I would personally recommend #2. After eating, it would be a little quicker to walk to MK from the contemporary than take the monorail, because the resort monorail only goes clockwise...so MK is 4 stops after the Contemporary, or about a 8 minute walk.
I wouldn't recommend leaving your car there, as it could well be towed. Back in the nineties, they didn't enforce this rule, and we saved on parking this way - but now they DO enforce, so be warned.