Here's a picture of the bottom area of my water heater showing the bypass switch in bypassed position. The other position (water heater in the loop) would be rotated 90 degrees down. The water comes from the left in this picture (note arrow on fitting).
Note: weasel-words added:
I should note, however, that my setup allows cold water to come out of the hot faucet even if the heater is bypassed. In other words, in my setup, regardless of the bypass switch setting...something will come out of the hot faucet. So, the bypass switch may not be your problem after all. Depends on how your trailer is plumbed. Check valve problems are a possibility as mentioned by others earlier.