In the map I'm making, players will have to choose which items to switch. In this case, I will clone the first block over to the side, clone the second block to the first block's position, and clone the first block to the second block's position. I know this works, however, players will choose which blocks to switch. In this case, whichever buttons they press will set up the command blocks to work. This means that I will need to add coordinates to a given command without removing the command. Is this possible?
I think you're going about this the wrong way. Instead of trying to change the hardcoded coordinates inside a command block, I'd suggest using relative coordinates and /execute. So when the player presses the first button, it summons an armor stand called Block1 at the location. When they press the second, it summons one called Block2. Then all you need to do is clone blocks relative to Block1 and Block2 and you've got what you need without modifying any commands at runtime :)