Melissa -

If you still can't get the handle off, it's likely that there's enough corrosion on the handle and/or stem to pretty much "weld" them together. This isn't really too uncommon with old faucets. If there was a screw in the middle of the handle that you were able to remove, that means the handle is meant to come off and yours "just doesn't want to."

Plumbers are divided about the best approach for this. Some seem to talk to it in the hope that it will change its attitude and become more cooperative; but this seldom works until the language becomes quite forceful and inappropriate for young ladies, and is accompanied by other displays of persuasive actions.

"Tapping" on the handle to attempt to "rock it" on the stem is sometimes claimed to eventually loosen things, and usually starts with light tapping but eventually moves to the "get a bigger hammer" approach. Sometimes innocent adjacent parts are injured with this method.

There are also numerous "soak it with &#||&$@#" where the potions used can be almost anything nasty. Since most waters that might have contributed to corrosion there are at least slightly alkaline, a mild acid like ordinary vinegar might possibly help to at least soften the crud, but most things aggressive enough to do much good are likely to make the stem unsuitable for reinstallation.

Some recommend applying heat, meaning with a propane torch or the like, but lots of walls have been set on fire with this approach, sometimes well inside where you don't see it until it's too late (and it seldom does any real good IMO).

IF YOU CAN GET TO the packing nut to get a wrench on it (see the picture at my link above) and can unscrew it, the whole innards of the faucet should come out quite easily, and you'll be able to deal with the handle and stem separately where you can beat it up without risking damage to the piping. Note that the packing nut should be a normal right-hand thread, but the faucet stem may screw out either way once the nut is backed off a ways.

Chances are that if the handle and stem are really stuck together as tightly as described, your best bet would be to replace the whole stem and handle parts, since any way you put the old ones back together they're gonna be stuck again very soon.

John