Walking distance the Doubletree would definitely be better. There is a gate at the back of the property that basically dumps you out right at the edge of SeaWorld property (it is a parking lot across the street, it seems to be used for employee parking and during busy times they will park guests there, it was in use during Christmas week). You walk through the parking lot, cross the street using a cross walk and a walk signal, and then follow the path to the main entrance.
Doubletree is also closer to Aquatica, you can use the same method to cross the street and then you turn towards I Drive and can walk to the entrance of Aquatica, again there are cross walks and lights across I Drive. This is a longer walk than going to SeaWorld but a much shorter walk than if you started from Residence.
Discovery Cove might actually be a little bit closer to Residence but I am assuming you would only spend one day there, while you would spend at least 2 days at the other parks combined.