Hi Jessica!
First, have you seen on the
runDisney Princess Half website that the Kids Races and Expo have changed locations due to a baseball game at the Wide World of Sports? Now, the Kids Races will begin at 8:45 a.m. and will take place at Epcot.
With you having a daughter in the 400m, a daughter in the 1 mile, and a son in the 200m, you will probably not be finished until at least 10:00-10:15 a.m. Assuming Epcot is open by then, you could hop on the Disney buses to the Polynesian Resort from the Epcot parking lot. You would probably get there quicker if you had a vehicle and were able to drive straight from the Epcot parking lot to the Polynesian. (simply because the buses run 15-20 minutes apart, and you can't guarantee one will be there right when you need it) I would think you could get there by 10:45, but I don't know for sure. If you can get a later reservation, then I would, but if not, you can always give it a shot.
I hope this helps! Please let me know if you have any other questions!