Well you need to figure out if you have a PRESSURE or a FLOW problem - not the same thing, but they are related. You can't get sufficient flow without sufficient pressure. An obstruction will cause a pressure drop which causes flow to drop.
So do you have sufficient flow using the onboard pump and water tank?
Do you have sufficient supply pressure?
You could get one of these for about $10 to verify your city water source can supply enough pressure with static flow:
But it's better to spend an additional $20 to get a good pressure regulator with gauge so you can limit the pressure on those city water sources which are ridiculously high:
https://www.amazon.com/Renator-M11-0.../dp/B01N7JZTYX
This also allows you to see what the pressure to your RV is when water is flowing.
So once you have the ability to verify good city water pressure, but you still don't have adequate flow from city water, but you do from your pump; I'd take a close look at the city water connection. It should have a screen and built-in check valve. It could be the issue. This video (starting at about the 2 minute mark) shows the valve disassembled:
If that isn't your flow restriction then it's time to start tracing piping.
If you didn't have good flow from your water pump either than you need to jump straight to pipe tracing.