| I bet hexus has it correct. Depending on how the receptacle and switch are wired it could be simple to change, or could require a new cable from the switch to the receptacle (or even running a whole new branch circuit). If the DW works with the GD unplugged, DW plugged in and the switch turned on, you need to turn off the circuit, then remove the switch cover plate. If there are only two wires in the box (black and white) hooked to the switch you have a switch loop. This is pretty common since the GD is not allowed on the kitchen counter circuit. If there is any other device in the box (like a receptacle) with the switch it gets harder to figure out what you have). You could still have a switch loop, or someone may have wired the GD onto the counter circuit, or fed another circuit into the box for the GD.
If you have a switch loop, power comes from the receptacle box up to the switch for control, and then returns to power the receptacle. This is easy to change so that half the duplex receptacle under the sink is always hot, and half remains switched for the GD. Identify the 'always hot black' wire coming into the receptacle. It is likely wire nutted to a white wire going up to the switch. The black wire that returns from the switch should be connected to the brass screws of the receptacle. You need to pig tail the 'always hot' so you can connect it to the other brass screw of the receptacle, and then remove the small tab between the brass screws. One half of the receptacle is now always on, and the half fed by the switch will work as before. Plug the GD into the switched half, the DW into the always on side. If power is fed from the switch down to the receptacle, you will need another cable to bring an 'always hot; line down to the receptacle for the DW. You also need to make sure at that point that the GD is not on the kitchen counter circuit.
It is not allowed to be, and the DW cannot be on that circuit either. | 
