Your problem is not the pressure but the flow. You have suffficient pressure to use even the upatairs fixtures but there is a flow restriction.
Think of your garden hose with a nozzle on it. If you open the nozzle all the way you have full flow; however, if you only partially open the nozzle you have the same pressure but less flow. Pressure comes from the height of the municipal water supply and is equal in all directions throughout the system (provided the distribution system is all on one level). Flow comes from the size of the supply line. A fire truck could not get enough water from your supply line to pump on a fire; but a 4" fireplug supplies plenty of flow.
I'm betting you have a restriction in your line somewhere that can be caused by several things: 1. A kink in the supply line (likely in a wall) 2. Using too much solder on a fitting feeds droplets of solder into the line which will accumulate and cause a blockage 3. Other trash of unknown origin in the line can accumulate and cause a reduction of flow.
If I open my mouth wide and blow out all my air it will not make much of a noise; however, if I pucker my lips or restrict the air with my tounge it causes a whistle. The same applies to your water supply systme. I suspect the restriction is at the main valve on top of the water heater. You can listen to that valve closely while others turn the water on in different places. If you hear a whistling or screaming from that valve, it may have the sloder droplets on the top of it. There should be a union nearby that you can open and check for the solder. But then, you said flushing a commode causes hot water at the shower, which means the cold water is obstructed at a point beyond the water heater; I hope you have access to that part of the line so you can check for solder.
A stethescope will help to pinpoint the blockage, or you can put a long screwdriver on the pipe, put your thumb on top of the screwdriver and your ear on the thumb. Let me know how you come out and I will work with you some more if necessary.