Sorry to hear about your "odor" problem. Maybe there is a local public fountain you can take a dip into!!!
However, the problems you describe are fairly common, but may be tricky to isolate. Let's try some basics:
Relieve the pressure from the bladder completely. Let the well pump fill the tank completely and bleed any air from the system using the faucets with the pump running. Again, with the tank full of water, close all outlets and charge up the bladder to about 60PSI. Most systems work fine between 45 to 65 PSI. Anything over 70 is pushing it. The tank needs to be charged when full, not empty.
Monitor the pressure as you draw water. Does the pump kick on constantly when the pressure reaches the low limit, and off at the high limit? This will help tell if the regulator is working properly.
Is there any pulsating water pressure at the faucets?
When you are sure you have a full tank, no air in the system, is your second floor water flow ample when the tank is reading 60psi?
There are a few "if's" here. Depending on how the pump behaves and the pressure responds, you have to determine if the problem is with the pump and volume of water being delivered to the tank, or if the pressure regulator is properly operating.
If you are still seeing any pulsating water pressure at the taps, then the bladder is water logged again. If the bladder pressure drops too quickly, then most likely the volume of water from the pump is low. The pressure should remain fairly constant at the tank if all the functions of the pump and regulator are working properly. Good Luck
You're adding more points of failure, and when the small tank runs out, you will see a temperature drop until the tank fills with hot water from the reserve. You also have to worry about eventually reselling the home. Given that, my preference is to keep it simple with a single tank.
One option to give you the same effect is a single electric tank with the lower element turned down. You are then only keeping half of the tank hot but can easily adjust it to have full capacity.
Best Answer
That appears to be a gate valve. There is a threaded portion inside the valve that goes inside of a block of metal that moves up and down when you turn the handle. Since you can turn the handle, but the flow of water doesn't seem to increase, the gate has somehow become detached from the screw. Maybe the threads have stripped out, or maybe the screw shaft has broken.
Even if I'm wrong about the exact type of valve, that one is broken one way or another and will need to be replaced. Ball valves are a good choice for water heaters because they tend to be less likely to stick and are easy to turn off (only takes 1/4 turn). This shouldn't be a big deal using modern push-to-fit connectors on that nice copper pipe.
Feel free to post an additional question if you run into problems with the valve replacement.
Now that I think about it... Before anything else, try to push down with a good amount of force on the handle while turning the valve to open it. Perhaps you can get the threads to bite down and pull the gate up.