Why does my water pressure drop after using my water hose for a few minutes?
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?