Water – Using a off-the-shelf pressure gauge to measure water pressure

The part that jumped out at me is this: "4" well with a submerged pump and a pressure tank in the garage."

How big is your pressure tank? My guess is that the greater water draw of a 1/2 or 5/8 inch hose can drain the tank in 15 minutes. The washer or shower has a much lower flow rate in gallons per minute used than a hose.

When the pressure is low from the hose, do you also get low pressure inside the house?

If you are on a municipal system and have pressure that high, you quite likely already have a pressure reducing valve (PRV) installed near your water meter. The International Plumbing Code requires PRVs on any water supply over 80psi. If this is the case, your PRV may just need adjustment. As they age, the spring regulating the device's operation can soften. Or it could be faulty and need repair or replacement. If you do not have one, you need to have one installed.

If you are on your own well with a pressure tank, the pressure switch controlling pump off operation needs adjustment. Other types of systems should have similar arrangements to control pressure.

How to adjust a PRV. There is typically a bell shaped housing with an adjustment screw and lock nut on top. Loosen the lock nut and turn the adjuster counter clockwise a small amount. The adjustment can be rather sensitive. Operate the faucets and toilets in your house to allow the system to equalize to the new pressure setting. Take a new pressure reading. How much it changed will give you an idea how much more adjustment is needed. Typical water system pressures should be somewhere in the 40-60 psi range. Shoot for the high 50's.

If the PRV controls supply to a fire sprinkler system (it normally shouldn't), you will need to check with a fire supression professional to determine if and how much you can reduce the supply pressure.

If you do need a new PRV, check with your municipality, they sometimes offer rebates to help mitigate some of the cost.