Patricia,
We are neighbors (I'm in New Jersey). Our situation is a little unique as when we were married, I was still caring for my elderly mother (who did not want to leave NJ), and my wife and I agreed I'd move to the Faroes as soon as I could. My mother passed away in March, so now we are moving ahead with my plan to relocate to the Faroes.
I believe it *might* be possible for you to apply for reunification while in the Faroes, but they recommend we do it while in the States. The form is on the Danish site, but you have to scroll down past the first Family Reunification link and go down to where it says "Faroe Islands".
https://nyidanmark.dk/en-GB/Words and Concepts Front Page/US/Diverse US/application_forms
Because I'm just starting this process now, it's kinda new to me too, but if I discover any "bumps in the road" or helpful tips, I'll be sure to share them with you.
Sam