Here's what I think is going on and how to handle it.
Drain your water heater.
Flip the valve Normal / Bypass to Bypass. This will bypass the water heater.
It sounds like you have a gravity fill port for filling the fresh water tank. Do not put the antifreeze in the fresh water tank. You will have a very, very hard time flushing it out when you are ready to use it again.
It sounds like you have a hose connection to attach a garden hose to the water system. When the garden hose is turned on, your water pump is turned off. And the water runs through your camper via the pressure from the water source.
If you flip the valve to Winterize/sanatize, you will need to attach a different hose. The hose should have the normal garden hose threaded attachment, but the other end should be cut so it can be stuck into the gallon size RV anti freeze.
You now turn on the water pump and it will begin to run, sucking the antifreeze up until the system pressurizes. The pump will shut off. You now go around to each faucet one at a time, hot and then cold and turn them on until clear water turns all pink. Then go to the next faucet.
If the pink stuff is pouring out low point drains, then the low point drain valves are open. Close them, or nothing will ever make it to the rest of the water system.
If pink stuff begins pouring out the bottom of your fresh water tank, then the in-line check valve between the fresh water tank and the pump is failing allowing pink stuff to feed backwards into the fresh water tank.
If you have access to the water pump itself, you might check to see if there is a separate valve there too. One direction would be for the fresh water tank, to suck water up, the other direction would be for the other "in" line that would suck water from the garden hose connection. (my best guess is, there is another valve there that needs to be flipped.)
The bottom line is, I really don't know how your system is designed, I'm only guessing how it might work if you have only 2 valves to flip.
My previous camper had a by-pass valve right at the water heater, and I added the valve to flip right at the water pump to switch from pumping from the fresh water tank or the hose that gets stuck in the antifreeze jug.
My current 5er has a valve for bypass (water heater), and inlet for winterizing (the pump sucks it up there), and another switch to fill the fresh water tank or run "normal" via the garden hose. If running "normal" via the garden hose, the water pump needed to be turned off.
So... bypass, connect hose and insert into antifreeze jug, turn on water pump. Turn on each faucet, one at a time. Try that, see what happens.