I bought a L5 propane tankless water heater from Amazon.com. It has a 37,000 Btu input (about 4 times the input of a typical 8,800 Btu 6 gallon water heater) and use this to 'warm' the water in the fresh water tank.
Living in the RV, I was really tired of getting home from work, and taking a 4 or 5 minute shower. It was 55F water going into the RV! So the 6 gallon tank got used up really fast! I started filling the fresh water tank with 100 gallons of 80F water. It would cool down to about 60F in 3 days, then I would refill it again. A side benefit was my basement storage stayed warmer, so did my bedroom above the water tank.
And I could take priceless 15 minute showers with all the hot water I desired!
The L5 is only rated at 5 liters per minute at 55F - 105F temp rise. The slightly larger L10 has a 55,000 Btu input. Both are sold at Amazon, but whatever you have probably will work equally well at filling the fresh water tank. Once your fresh water tank is warm, you could use the water pump only while she takes the shower, or if not enough flow or pressure, then turn on the fresh water shore supply line about 1 turn, so that it will be say 75% warm pump water and a little of the cold city water supply to increase the gallons per minute flow a little bit (without overcooling the supply water).
I could have piped the L5 inline with my motorhome fresh water connection, however I am not sure how well it might have worked. IF I ran a lot more than the 5 LPM that it is rated at, then the water would be 'cool' but not 'cold'. So it might have heated 2 GPM from say 55 F ground water to about 75 -85 F supply water. Problem being that if I am in the shower, I did not have anyone who could adjust the L5 gas valve (it is variable) to change the supply output water temp down to say 75F. 75F would be ideal, as I would be mixing 75F water about 50% with the 140F 6 gallon water heater tank water and get a 2 GPM shower for 10 minutes before it started to get cold! My worry was that if flow is say 3/4 GPM, the L5 can warm the 55F ground water to 110F and that will scald me, just with the 'cold' water on. If I had someone to adjust the regulator, it might have worked out fine, with the L5 inline with my fresh water hose, into the city input of the RV. Just have someone adjust the shower flow, then move the regulator up or down to keep the output water 'warm' but not to hot.
I already have a 5.7 GPM variable speed water pump, so flow was not a problem in my situation. I also have a 100 gallon fresh water tank, and could fill it anytime.
The problem with RV tankless water heaters is that the flow changes SO much in a RV, it is not a stable 40 PSI or unlimited water volume. Sure it is 'fine' in a RV park, where you have no concerns with using more water so it will come out cooler, but with limited grey capacity, and fresh water tank size, you are limited in the amount that you can adjust volume, and still conserve water.
Also tankless systems rely on the fresh water being a certain temperature. If you are in Florida, they work great with 65F fresh water. Oregon has a average ground temp of 45F. So the output water will be 20F cooler while in a RV park in Oregon than while in Florida.
That said, there is one brand RV tankless water heater that has several sensors, and variable gas flow. It will detect the water temp mid-heat exchanger, and adjust the gas volume and flame size to only warm the water to about 110F regardless of flow in GMP. It also has a large enough burner and heat exchanger to warm a larger volume of water, even if it is 45F input.
Most RV tankless heaters have a sensor for flow. When flow is detected, it will light the burner and run until the flow stops, or the output temperature limit exceeds about 115F. The RV owner is 'supposed' to increase hot water flow to the point that the water heater is only 'warming the water to 105F'. Yet if they decrease flow a little bit, or the pump is running slow today, it can quickly reach 110F and shut off, then flow 55F for a few seconds where the owner starts to scream! At which time the output is less than 110F and the burner will light in a few seconds, put out really hot water again!
Have fun camping!
Fred.