How to remove super tight sink faucet supply hose nut

While I hate plumbing, I do quite a lot for close friends and family. I don't know exactly what you are doing, but I know a couple of things, and I hope these will help. When you loosen the gland nut closest to the wall, you probably need to turn it clockwise. Normally when you loosen something, you usually go counter-clockwise. In this case the nut stays on the pipe, not the valve. Always you a back wrench like you were talking about to keep from twisting the pipe.

Here's a You Tube video that shows it. I hope that this helps and is not exactly what you have done before. Did I say I hate plumbing?

That part is called the stem, and is typically fully replaced, or more often, you simply replace the o rings and, well, as noybman mentioned, the bushing(s).

I have a feeling, if you pull the stem completely out, you'll fine the little brass part you're really looking for. There's a base at the back of that stem that closes the valve, and it will be replaceable on some spigots, in whole or in part. If yours is replaceable, it is typically adjustable as well.

Do a google image search for your spigot under 'repair kit'. You'll get a very handy diagram.