If I want to remove a soldered joint in a shower valve by heating it and pulling it, would that heat cause damage to the other soldered joints about 2-3" away on the valve?
Not really, the key is to be directed in the application of heat to the required joint, Almost certainly you will melt the solder on the adjacent joint, however the solder should re-set quick enough. Bigger concern is to make sure you don't apply too much pressure to the fixture and dislodge the loose joint (at heat) --
Remember, the solder should not be contaminated and should re-set well enough.. the nice thing is that its pretty easy to test (i.e when you turn the tap back on) - If you are concerned, or there is a leak, you can simply add more heat and apply some solder with new flux.
It's possible, the trick in this case is to apply lots of heat quickly and remove the appropriate fitting before the heat has a chance to conduct to the other fitting. The solder will tell you when it's ready by glossing over. I'm trying to think of this from a DIYer point of view. I could imagine a small torch heating up the fitting for a long time allowing the secondary fitting to sweat loose. Avoid taking your time with it.
Method A: Proceed as if intending to remove both soldered joints at the same time. Heat them both evenly. For reassembly, prepare both and re-solder them at the same time together. If there is a valve cartridge assembly (such as a shower control) involved with either, remove that so heat doesn't damage it.
Method B: Try to reduce the heat transferred to the adjacent joint. Two inches away with copper pipe will be challenging no matter what—copper is an excellent thermal conductor. I'd clamp on several vice grips and tightly wrap soggy wet rags around the pipe and adjacent joint. That certainly would keep it getting near solder melting point. But it also will interfere with getting the target joint hot enough to do good work.
Could, but you could also keep the joint(s) cool with a cold wet towel.