Flushing the system by using the city water connection won't clear out the water pump, you also don't want to send any antifreeze or bleach into the water heater. First change into clothes that you don't care about, then:
1. Fill the fresh water tank, adding 1/2 cup of bleach during the fill process.
2. Open 1 of the low-point drains, turn on the pump until it runs clear, turn the pump off, close the drain (turn the pump off first or you will spray yourself with bleach water trying to get the cap on).
3. Open the other low-point drain, pump on, run clear, pump off, close the drain.
4. Pump on. All the remaining steps assume you keep the valves open until they run clear.
5. Hold the toilet flush valve open.
6. Open the shower cold valve, close, then do the hot water side. Don't do both at the same time, you won't know if one has run clear and the other hasn't. If your pod has the mini-sink in the shower, do the same with it.
7. Do the same with the kitchen sink.
8. If you've added any other water connection (I added an outside shower), do the same with it.
9. Turn off the pump.
10. Top off the fresh water tank.
11. Wait at least 3 hours, preferrably overnight. You now have bleach in every possible nook which will sanitize the system.
After 3 hours or the next day:
1. Drain the fresh water tank using the drain hole on the bottom.
2. Refill the tank.
3. Repeat steps 4-9 from the last checklist (I would skip the low-point drains, but you may not want to), waiting about the same time on each valve that you did when you were waiting for the pink to disappear.
4. You may want to repeat steps 1-3 once or twice more, I don't. I let the remaining bleach odor just work its way out during the first trip of the season.
5. Now change the valves on the water heater - hot and cold lines parallel to the water pipe, the valve in the middle perpendicular.
6. Open the hot water valve on the kitchen sink. Wait for the air sputtering to stop. Your water heater is now full. I would let it run another minute to flush it out.
7. Either top off or drain the remaining water in the fresh water tank as desired.
Seems like a lot of steps, but the "day 1" checklist only takes 10-15 minutes. "Day 2" is maybe 15-20 depending on how many times you rinse the system.
All that said, I plan on cheating this year. The RV antifreeze is in the alcohol family (which is why it doesn't freeze), so everything but the fresh water tank should be sanitized already. I drain my fresh water tank and the feed line to the pump just as much as possible in the fall so I'll probably just fill it, clear out all the antifreeze in the pump and water lines using that water, and then drain it. There's little opportunity for something to grow in the tank and certainly no way for it to grow in the water lines.