I have a very small drip from a new galvanized union. It's the horrizontal hot water line that feeds into a shower faucet. I believe the new and old pipes are just a hair off and I believe that's why the union leaks... However getting to the old pipes and replacing them would take a lot of time I don't have. I'm doing this for my mother in-law and I've already spent several days and hundreds of dollars fixing the pipes in her bathroom. Do you know of any way to fix the leaking union such as an epoxy or stretch and seal tape?

I would start by simply undoing the union, coat the threads with a liquid pipe lubricant/sealant (like rector seal) and tighten it back up using pipe wrenches. The lubricant will allow you to tighten the joint more without the threads binding. Give this a shot first, and really crank that sucker down. Let me know how things work out.

MGD gave you great advice. Just for my own curiousty if you enscrewed the two halves of the union how far apart would the two pipes be? If the soread is too great you might have to use fittings to mate the two halves.