Lemme get this straight: the bike has grip-shifters? On a 3 speed? I haven't seen them, but that doesn't mean they don't exist. Are you sure that the shifter is meant to work with that model of 3 speed hub?

Where are you having trouble tightening the cable? Normally the way to tighten it is to put the shifter in the position where the cable has the most slack possible. Then pull the end of the cable as tightly as possible and tighten down the attachment point on the hub.