Mary couldn’t unscrew either of the two outlet hoses emerging from one of the (many) Y valves in her Vassar Farms plot. After deploying the Lesser Vise-Grip from my bike toolkit to no avail, I brought a Greater Vise-Grip from the shop and applied brute force. During that process, the plastic inlet hose fitting ripped off the valve and sprayed all but one of its latching teeth across the plot:

As it turns out, the male outlet hose fittings on all the metal-body Gilmour Y valves in the plot have corroded:

The scarred knurls show the force required to break the brass hose ring loose and unscrew it:

Some of that crud may be hard water deposits, but the destruction of the male threads seems like a galvanic reaction among all the various metals in play.
The male fitting began rotating in the valve body, so I crushed it in the bench vise to make more headway. While I had the victim clamped down, I hacksawed a slit through the housing, pried back the edges, and freed the parts for one leg of the Y:

You’d think “not corroding” would be high on the list of attributes for a garden hose valve…