Hi bobsue2,
The fitting you're showing looks like a fresh tank overflow drain. It also appears to be by the rear axle. The fresh tank is usually located over the axles.
With the 4-way Anderson Valve, water filling the fresh tank is under pressure and when the tank is full, it has to have a place to go.
Your shower on a Key Largo is forward. It and the gray #1 tank it drains into are located in the forward part of the trailer, in the drop frame area. So the slow shower drain is probably unrelated.
Take a look at the shower drain. The drain cap should lift out easily. I put a small screwdriver into one of the drain holes to lift it. You may have a buildup of hair in the drain fitting under the cap.