Hi & welcome!
The hot & cold low point drains are usually side by side, so odd that you found only one. And you said "under the faucet". Is that where the valve is, but the tubing continues on through the floor to the outside?
What other valves are you expecting to find? Outside there should be two large T-handle valves to dump the waster water tanks. They may be behind a door that opens from the outside, or may be simply protruding from the waste pipe under the trailer. You may also have a shut-off valve that enables fresh water to flow from the city inlet to the fresh water tank (but not all trailers have that).