You can hop a bus from the resort over to the MK, or if you are up for a little walk you can walk through Epcot and hop on the monorail. This is sometimes harder to do if your children are little because the walk is long. this is a great place to try and get the front seat of the monorail, it is a longer drive and the kids will love having the front seat. You can always stop at the bakery at the Boardwalk and buy them each some sweets for the walk or save them for the monorail drive. I know that is an incentive that would make me agree to do the walk.
I try to do the walk through Epcot, and I always walk from Boardwalk to MGM while the family takes the boat. I always get there first and I had some much needed exercise.
If the children are really young you might want to take the car over. This way you can leave when you want to without having to wait for the busses. But then again, you would have to wait for a tram to take you to the parking lot.
The Boardwalk is one of the first pick-ups so you can be assured of getting a seat, when I stay at Beach Club Villas we are the last pick up and the bus is sometimes full. Peggie