When you re-sweat joints, do you have to remove all the solder when you are cleaning the area to be re-sweated?

No, but you have to clean it enough to get the fitting on.

If I have to reuse a fitting that's already been soldered on I heat the fitting until the solder gets runny. I then take a rag and wipe the joint clean. If you do it right and don't leave any bumps or ridges the fitting will be tinned and slip right in.
Good luck, Tom