UPDATE
2 Frazzled got me on track!! I checked the tubing and connections from the fill connection up to the outside shower head. No problems found. The shower puts our a more reasonable amount of pressure than either sink. The shower in the bath puts out fairly decent pressure. The plumbing for the outside shower, the shore input and the lines to the bathroom sink can easily be traced in the cabinet under the sink by removing a panel.
This morning, our home water pressure was 90 psi. It was mid morning and the pressure was higher than our normal 80 pounds. I rechecked the inlet backflow check valve, my hose regulator (reduced the 90 psi to 45 psi) and rechecked the water flow at the sinks. it still is a lower flow than it should be in my opinion.
Then, I recalled when we moved into this house years ago, the shower head put out a lower flow than we wanted. I remember I took the thing apart and redrilled the hole in the end of it slightly larger and got more water flow. So, thinking about that, I removed the end of the kitchen faucet (the part that has the flow aerator and screen). Inside there is a small plastic disc that has a hole in the center 1/8 inch in diameter. That reduces water flow and stops surging. Well, both of mine in the sinks now have a disc enlarged to 3/16 diameter because that is the size bit I used to drill it out larger.
The result was a significant increase in water flow at the sinks. Now, as to the shower, I never use the outside shower. Never have used it. The shower head in the bathroom was replaced when we first got this rig with a sink sprayer like this
https://www.amazon.com/LDR-501-6200-Sprayer-Replacement/dp/B000I1AQWIThat is an old Class B trick. They are instant on and off and don't drip like most shower heads. Class Bs can have pretty small tanks and these things can save a lot of water when boondocking because they don't drip. I modified it slightly by taking it apart and drilled the water passage way a little larger.
Now, I think we can do just fine hooked up to water, although the water flow when on the pump is still a little greater than when using shore water.
Problem solved! Now, on to a few other things prior to going on trip for a couple of weeks.
Thanks for everyone's input.
Paul