[JRTJH]

Often Keystone routes water lines near the "un-insulated steel chassis rails" in the basement and above floor, they run them near the side walls, inside cupboards where it is difficult to force heat from the interior of the trailer cabin.

If you haven't yet opened all your cupboard doors slightly, you might want to do that to allow heat to reach the backsides of the cupboards (against the trailer sidewalls).

Sometimes there's nothing you can do without removing the underbelly cover and physically repositioning the PEX water lines, but in the meantime, I'd open the cupboards, get some heat into the areas where you see "above the floor PEX lines" and, if you have an outside shower, open that door, try to insulate the faucet by putting a towel or some bubble wrap in the space and closing the door. On the inside of your trailer, locate the backside of that outdoor shower and make sure there's heat available to that area. Essentially, if those "branch lines freeze behind the outdoor shower" you'll disrupt water flow beyond that point. Since it's "open to the outside and unprotected" you can imagine how easy it is for that faucet to freeze....

As for leaving a faucet open and dripping to prevent freezing. Remember that in an RV, what goes in must flow out, so if that dripping faucet is going into a closed holding tank, it's subject to overflowing.... If you leave the holding tank dump valve open, then the dripping water will flow out of the tank and into the 3" drain hose, which is not insulated. If it's cold enough, that drain hose will start to freeze and as the "drips enter the drain pipe" they can freeze, eventually completely freezing off your entire dump hose... That will mean that nothing else flows through the hose and, like the full holding tank, water will back up and can flood your trailer interior.

So, most people don't leave a faucet dripping in an RV, it can lead to much bigger problems than the inconvenience of a frozen PEX line to a single faucet.