Glad to hear that the Lincolnwood is up and running (and that your 'other half' seems reconciled to the idea of being a two-organ family!
As long as there are no extremes of temperature and definitely NO dampness, the Citation should be OK in store in the garage - covered over, of course.
Desoldering requires heat, full stop. You'll need a soldering iron. If you're unsure about using one properly, get an old radio from a junk shop and practice de soldering and re soldering components. Make sure the iron is powerful enough - temperature controlled ones are great too - and use a solder sucker to remove old solder. When soldering, remember to heat the joint, not the solder, and be careful when soldering components easily damaged by heat, transistors etc.
Of course, if you know all this already, tell me to shut up!