Laura,
You do not have a problem with your coach. The issues that you described are related to low pressure or excess restrictions in the city water supply. If the city water supply has adequate pressure (above 65 PSI), your filters and water softener are creating too much restriction to give you the flow rate that you want. So the pump is removing water from the tank to supply you with water thus lowering the tank level and triggering the fill solenoid to add more water. So the correction is to fill your tank, turn off the fill valve until the tank gets low and then refill the tank, but do not leave the fill valve (or autofill) turned on unless you need to refill the tank.
Gerald