You need a new boyfriend.

Righty-tighty, lefty-loosey. Use one wrench on the faucet to hold it and one on the hose and bear away. if you ruin it... well you were going to replace it anyway.

This kind of stuff happens. DH couldn't get a valve under his mother's kitchen sink to budge. Called in a plumber and with all the tools available to him, he couldn't get it to budge either. He had to call in a second guy to help him. And even then they worked for some time on it and I think they ended up cutting it off.

try some wd40 overnight...and try again.

Not a boyfriend. You need a manfriend.

Penetrating oil overnight.

You could even try heating it with a propane torch. Judiciously of course, and it does depend on the surroundings. I'd first cut the hose off the stuck coupling.

If you can't unthread it, one time I used a hacksaw to cut through the metal of the hose-end coupling, then peeled it back a bit, then it unthreaded off with vise-grips.

"If you can't unthread it, one time I used a hacksaw to cut through the metal of the hose-end coupling, then peeled it back a bit, then it unthreaded off with vise-grips."

The threads on a hose coupling play no part in sealing the joint except to hold the hose washer tight against the face of the hose bib.

Slight damage to the threads from making a cut through the coupling will not cause a problem.

WD-40 is not a penetrating oil and will not do very much.
Auto parts stores have decent penetrating oils.

Liquid Wrench remains the old standby, but it works better on steel fasteners than brass or copper.

If you have high alkaline deposits in your area,(white deposits around the connects), you might try some distilled vinegar soaking awhile if possible.

I've tried the Liquid Wrench. The problem is that the connection is in a small niche, and they are at this angle that makes getting liquid up into them difficult. I actually tried to "inject" the oil into the connection using a hypodermic needle and syringe, but it didn't seem to work - I could see the oil just pooling and running down the faucet. I may try to heat it.
I do appreciate all the advice!

If you are trying the propane heating method after you put oil on.........well,, I wouldn't do that....especially what happened the first time. It was real exciting though.

Here's the outcome, $150 later! I had a plumber over. He managed to remove one hose from the faucet using a LOT of strength (and he turned the water on and banged the faucet to loosen things). The other faucet - well, the hose wouldn't come off and he had to replace the whole bib/faucet thing. Now I can do laundry. :) Thanks again for all the suggestions!