12volt RV pump in a two story house.

I'm revisiting a previously discarded idea of  using rain water for my toilet and laundry.
I'n doing so I realized that both the toilet and the washing machine were built to use pressured water, so a header tank would probably be insufficient.
I'm considering a pressure sensing pump as the fix for this issue.
The ones designed for RV's have a good price point, but don't seem to list their "head".
The bathroom and laundry are on the second floor and rainwater storage would be in the basement, so the challenge would be significant.

I have a sump pump that I think would be up for the challenge of lifting water that high.
If I use the sump pump to fill a header tank that in turn feeds the RV pump, there would be no head for the RV pump to overcome.
Alternatively, the sump pump could be fitted with a pressure sensor.

What do yall think makes the most sense?

Is there a reason for 12 volt? A Shurflo 2088 has 60psi and a vertical pump distance of 12ft. so probably getting to the max distance of your tank or washer for a one floor push. They acctualy make mini pressure tanks for rv's which might help get it up to the second floor.

Yeah the 12 volt ones are about $100.00 cheaper than a Shurflo 2088.
I figured I could start without the accumulator tank and add it later if they system works out.
I have a couple of Zoeller sump pumps that move 90gpm, up 18' of head.
They are sized for 2" pipe, but I could use reducers.
Using them would be ideal, but they are obviously not designed for this application.
I think I have a  120v pressure switch, and I wonder if I would need a pressure tank, or would an old , defunct water heater do the trick?
I think a check valve would be necessary either way.

A shallow well pump from Harbor Freight (linked below) with a built in pressure tank will pressurize the line to 55psi and is actually made to do what you are looking to do.  I have one to run our irrigation delivery system from our rainwater storage and have read a lot of folks use the same pump for irrigation and off-grid water delivery.  It's listed for $179 but goes on sale occasionally or with coupons you can often find it for about $150.  There are reviews of it on youtube you can find pretty easily.  Just another idea I guess.

Harbor Freight Shallow Well Pump

I suggest using 1 inch pipe around the house, it vastly reduces the pressure losses and maintains a good flow as well.