There Is Always A Solution
If you haven’t read the Plumbing Problem yet, then read THIS before you read the answer!
Did you guess why the gauges were reading different numbers?
Here is what was happening:
The pressure gauges were BOTH right - there was high pressure in my Mom’s water lines (and the neighbors) but low (40psi) pressure at the gauge next to the pump.
The reason the pump pressure read too low is that there was pressure-loss (probably due to gunk build-up) along the short line from the pump to the gauge and pump switch. The pressure in the rest of the system was very high.
The problem was getting worse with time
The gunk build-up meant that the line controlling the pump was reading too low. Therefore, the pump switch, set to turn on when the pressure fell below 40psi and off when the pressure rose to 60psi, kept turning on because no matter how much the pump worked, the pressure at the switch never read above 40psi (if you aren’t fluid dynamic savvy, then think of this like a hose with a kink in it - when it is straightened out, the pressure is high, when it is kinked, you get just a trickle of water). We had a major blockage which acts like a kink.
So… the pressure just got higher and higher. The reasons that everyone’s indoor pipes didn’t burst are:
The burst at the value outside relieved pressure
Mom (worried about the high pressure despite being told not to) turned on indoor faucets
Because Mom wouldn’t let the problem go, we caught it in time.