I recommend paying for VIP parking, which will help you get even more of a head start. It certainly can be a premium charge (about $45 to $50 per day), but at a park like Magic Kingdom, it will help you save major time.
I recommend renting a stroller, which costs about $15-$30 a day, depending on if you need a single or double stroller. No more chasing the kids! You’ll be able to strap your kids in and zoom around the park way faster.