Water system in my Coleman pop up not working

A pump problem then, not a city water issue.

There's a clog in the shut off, line to faucet, or in the faucet cartridge ... hook it up to a supply tube on another faucet, it connect to a garden hose to check if faucet is problem.
Water pressure problems on following link:
http://waterheatertimer.org/Low-water-pressure.html

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Well I see from the way this unit hooks up it will put a back pressure on the faucet valve so I would take the handle off and then turn the faucet on with the stem and see where the water is coming from. It is possible that the retaining ring for the faucet cartridge is loose or the back pressure has forced a seal out of place. I know this does not explain why it does it only when it is hooked up but you need to get to the area where the water is coming from.

it is likely required. many new faucets have what's called a pressure balance valve that helps prevent scalding by lowering the pressure of hot when the cold pressure drops (due to a toilet flush or other water being run). Because you have pressure to only one side, that can cause the valve not to provide the necessary volume.

This sounds like you have an inadequate supply of water to the unit. Make sure your supply faucet is turned all the way on, use a 5/8 or 3/4" hose from the faucet to the unit, and use a smaller tip on your spray nozzle to minimize the amount of water you are using when working.

Take the water saver out. it restricts the flow of water. it is underneath the screen. Unscrew the spout and take out the screen. above the screen there's a little piece that's round with holes in it. Remove it and put the spout back together. hope this helps!

it souns like a factory flaw in the piping or whoever hooked it up, over bent or kinked the line

There is generally a water pump fitted. In the early days of campers the water had to be pumped manually by either a foot or a hand pump and later people grew lazy and so electric pumps were fitted. At first these were controlled by a switch or button close by each faucet and needed to be held pushed in for water to flow - for obvious reasons the flow stopped when the button was released.

Later people grew impatient as well as lazy and also tended to be slightly wealthier and liked to take a shower so the system was automated. The electric pump was integrated with a water pressure switch so when a faucet is turned on the water pressure fell and turned on the pump and when the faucet was turned off a significant pressure would build in the pipework, sufficient to cause the pressure switch to turn off the pump.

The scope of the equipment varies a great deal depending on the amount of water carried, the size of the camper, the hot water system and the price range and could be anything from a single submerged pump to a multipump system to provide a luxury shower.

I suggest you obtain a manual or owner's handbook in order to discover the equipment fitted to your camper and how to operate/troubleshoot it. Such information is of particular importance if the camper will encounter freezing temperatures during the winter lay over. Failure to winterise properly can cause a great deal of expensive damage.

If it leaks while filling it is likely any of the several fittings or it may be the 3 port check valve attached to the incomming water line. These are routinely installed backward. The idea is that when hooked to an external water supply the water goes only to the faucet and when using the tank, water can only go from the tank to the faucet. You cannot be hooked to external water and use the tank.

Any cracks in the tank should be obvious.

Use teflon plumbers tape on all screw fittings or will leak for sure. Hose clamps are also a necessity.

http://www.coleman.com/coleman/images/pdf/2300-700.pdf
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