As near as I can tell, that ring was attached to the Y adapter, and used as a grip. So I’d expect that it would turn in the same direction.

I may need bigger channel locks, as the ones I own aren’t big enough.

Trust me...you want the Y and the ring to turn in opposite directions. Or at least you want to be able to hold the Y in a fixed position while you unscrew the ring holding it on. If you turn both of them in the same direction, you won't be able to undo it.

So which way do they turn? And how does that work, since the faucet is a third thing, which presumably shouldn’t turn at all?

Does the ring unscrew from the faucet? Or does the Y unscrew from the faucet?

Right now, the ring seems to move freely.

The ring should unscrew from the faucet spout. Let me understand what you are saying for sure. Does the ring turn freely and the Y doesn't, or does the Y also rotate when you turn the ring?

The ring turns freely. The Y is frozen.

The ring may be designed to spin. Grip the yellow ring with the proper tool, are you able to grip the yellow ring with you hand, then grip the y with the proper tool, turn in opposing directions.

I do not know you, but I would have not used PB Blaster.

Maybe you help us help you....how old are you, what is in your tool kit.

I am concerned about your mental and physical health, if you are able to live alone.

I purchased a place, whose owner was unable to deal with maintenance.

If the ring spins freely, something is likely broken internally. There are several designs for these, but I suspect there is a threaded female fitting underneath the yellow ring and the two pieces are supposed to be firmly connected. If someone in the past tightened the ring too forcefully, it could have broken the connection between the ring and the fitting so that the female fitting is just sitting there and the ring is spinning rather than turning the fitting. Sometimes this happens when people don't have a washer in place and over-tighten the connection because there is a leak. I don't know how handy you are, but I can think of only two ways to remove this:

1) Get a Vise-Grip, put it pretty tightly on the ring, and try to unscrew it. The pressure from the Vise-Grip may be enough to turn both the ring and the fitting underneath it at the same time.

2) If the first method fails, you would need to cut off the ring; then you will have access to the fitting that is screwed onto the faucet spout and you can unscrew it directly (probably with a pliers).

@kudzu9 Your analysis makes sense. I’ll check whether my vise-grips are large enough to reach around the ring. But I’m guessing that I’ll wind up with your second alternative.

Good luck.