Tap mixes warm into cold water

Do you have an out side shower? is it turned off at the faucet handles or just the shower head? If just the shower head it will back feed to the other faucets.

Your faucet is worn internally....seals bad allowing hot/cold to mix.

RV OEM faucets are typically cheap junk faucets..replace it with a good quality residential faucet.

You need to adjust your faucet internally. You should have a allen wrench to remove the handel. Check the net for instructions.

Are you sure that the hot water is not the water that has been heated by the sun and is in the hose to the RV?

It wouldn't be the first time I saw reversed lines. But what do you mean by warm? Are you on city water or the fresh water tank. I know when I use my fresh water tank the cold is not really cold but ambient temp (warm). If not that, probably just a messed up mixer valve in the faucet.

Check the hot water tank bypass valves. The valve on the by pass line may be open is my guess.