Larry
I've a similar setup, but without the valves from the Tees to the
heater. (I figure if a hose breaks, I could just replumb the existing
hose. Actually, I didn't figure anything--it came that way! I
leave the valve across (the middle in your diagram) open most of the
time. (if it's winter and cold and want some hot water fast, or the
engine is not getting up to temp, I close it, but that's rare.)

It sounds like your valves a little different though--If I had three
valves and shut them all off, then there would be no coolant
circulation on my system or engine. I'm also not sure I understand how
the water heater bypasses the thermostat and heat exchanger. My
coolant runs:

engine - water heater (with bypasses) - heat exchanger

part of my problem is that the wtaer heater hoses are smaller than the
engine hoses, so obviously I need something to give there, thus the
bypass. Here's a diagram: (best viewed with a fixed-width font)

WATER HEATER
: :
: :
engine......____L___/___L____......heat exchanger (to engine)

Of course, the heat exchanger is mounted on the engine, but it's hard
to loop with these text diagrams Here ... and : are hoses, _L_ is
a T and _/_ is a valve. I have no valves between the _L_ and the heat
exchanger.

mickey