I am new to soldering and am wondering if I solder to a fitting with an existing soldered joint will the heat re-melt the solder in the first joint?

First off, I should point out that the ideal procedure is that when soldering a given fitting, you should solder all of the joints made with it at the same time, so as to avoid such problems.

Having said that, I wouldn't worry too much if I were you - even if an existing joint does melt a bit, as long as you don't mess around with it, it will re-harden into place just as it should.

Have fun!
Moishe

Part of the reason a plumber would get $50-$100 for a 5 minute job like that is that it would take him 5 minutes. Experience and aptitude count. Try it. If worst comes to worst, you can give up on it, and go buy a Shark Bite fitting. $10 or less gets you system back together. Try wraping wet rags on the joint you don't want to come apart.