I think the easiest thing for you to do,
@Haley R, monorail over to MK and boat or bus to the Fort. There is a newer childrens playground just up from the boat dock at the Fort that sounds like it would suit your needs. It's just off the dock between the Settlement Trading Post on the left and Trail's End restaurant on the right.
If you bus in from MK, walk down towards the lake in front of Pioneer Hall and Trail's End and you will see the playground on the right.
Bama Ed