Welcome to the Disney Parks Moms Panel, Carolyn!
What a fun day your grandchildren are going to have enjoying
Magic Kingdom Park on their own. I also know it represents a bit of a challenge for you with dropping off and picking up. Luckily, I'm here to help with some advice to make your experience as smooth as possible.
The guest Drop off/Pick Up location for Magic Kingdom Park is located in the lot adjacent to the Transportation and Ticket Center, just follow the signs and they will guide you through the loop - I've had to drop off here before myself, it's relatively easy, especially if you choose non-peak times to drop off/pick up.
Your grandchildren will continue their journey to the park by proceeding into the Transportation and Ticket Center and boarding the Express Monorail to Magic Kingdom, or the Ferry Boat to Magic Kingdom. They will also need to repeat this process at the end of the day, so make sure they consider this transfer time when you set the pick-up time for them - it will likely take about 20-30 minutes for the return trip to the Transportation and Ticket Center for pick up. Also, if they use the Monorail to return, make sure they use the Express Monorail and not the Resort Monorail. Both will end up at the Transportation and Ticket Center, but the Express Monorail goes straight there.
I hope this helps, Carolyn! Please let me know if you should have any additional questions. I'm here to help you navigate the new experience of helping get your Mouseketeers to Magic Kingdom Park.
Faith