Can you provide any pictures or a more detailed description?

I presume these are normal threads and you *are* trying to turn the wrench counter-clockwise to loosen, right?  :-)

It sounds like there may be corrosion involved, which will make it difficult to loosen. It could also be good old-fashioned pipe-dope that is thoroughly set and hardened.

A longer handle on that wrench might help (Archimedes, levers, etc.).

Also, impact can help a lot. Tapping it with a hammer while trying to turn it might do the trick. Or pounding the handle with a hammer in a counter-clockwise direction might do it.

Once you get it to *start* turning, the rest should be easier.

Of course, depending on your tolerance for replacing part of your plumbing if it breaks, enough raw physical force can solve a surprising number of problems...