The Grandstand area (primarily the 8000's) will be pretty close to the Carriage House (check-in) and boat transportation to DTD. The Congress Park area will put you the closest to DTD. If you get in the 1500-2500 numbered rooms that should put you in the middle of Congress Park and close to that particular quiet pool and almost equal distance from the Carriage House and DTD.
Some of the quiet pools have some kiddie water play areas, the main pool does indeed have an area and has a zero entry area into the main pool. There are some playgrounds around the park. You can rent bikes, surrey bikes, fishing excursions, mouse boats, tennis, basketball, and there is a spa.
HTH
P.S. - Having a one bedroom will completely spoil you!