The cold and hot (blue and red) come from the back of the trailer. The picture shows incomplete plumbing, there are now two lines going up to the sink hot and cold faucet. There are also two valves that allow for draining each line down through the floor to winterize. When they are closed, pressure is maintained to the kitchen faucet.
If you look, there is one line that is the translucent tubing with the white cross hatching. That is the output of the water pump and it is cross connected back into the cold water supply. The idea is that if you are on city or park water, you close that valve and the water then can only go up to the sink. If you are running on the pump, you open that valve and then the cold water can go back to the sink as well as flow back aft to the rest of the system including the hot water heater.
The valve also serves another purpose, it isolates the pump and tank so that when you are on city water, the tank does not backfill, even if there is a check valve in place. As far as I know, this was the original setup with the copper plumbing as well. It may not look like it, it was much more of a mess when I first started working on it and it took some head scratching to figure out how they had it all connected.
Hope this helps, feel free to ask any more questions.