The power cord on the dock is a standard appliance cord, sold on ebay
etc. with different plugs for different countries. They come in two prong and three prong types. Used on laptops, printers, etc. The end is soldered inside the dock or attached through a standard type of plug on that end. I do not know exactly which part these Botvac
docks have, you can compare to pictures in catalogs.
The entire cords are no more expensive than the plug adapters for different countries.
Sounds like your dock is defective in this part and should be replaced, unless you like repairing things yourself. It should be under warranty. The problem could be in the dock connector and not in the cord -- depending on which wiggle makes it work.