We rarely tow with a full water tank. Our tank on our Forest River is inside under a bench seat, so no real worry about it going anywhere.
The tank is in the front left corner, so if I tow with it full I try to put some weight opposite it in trailer to try to balance things... but it is not that big a deal, it is only a 30 gallon tank.
We usually carry a 5 gallon freshwater cooler in the truck for drinking water, as the water in our camper has always seemed to have a "plasticy" flavor to it.