I would like to replace my faction's HQ with another. So the process would be recycle the old one? Then I get a Faction HQ Datacard. Is this a special kind of facility? What if I already built a Palace in a place I want and just wants to designate that as my new HQ? Or once I recycled my HQ, the only thing I can do is build a new HQ from scratch?
During the period that your HQ is wrecked to when your new HQ is completed, your faction will have a lot of features annoyingly disabled, so I wouldn't recommend it.
A better solution is to try to hit the next membercount level for a new HQ DC. All you have to do is remain at that level for a day and you should get an extra DC.