Hey Shimara,

Your best bet would likely be to keep the personal house for now, and try to purchase another one for the FC. Then if you really want the FC to have that particular plot that you purchased first, you can demo and relinquish the plot, and then relocate the FC house instantly. If you relinquish the personal plot you have now, you'll be subject to the random timer again before you can repurchase for the FC, unfortunately.

I know Jojoya posted something like this already, but just thought I'd give more details!