I just solved my own problem and will post in case it helps someone else. Even though, I’ve been able to play Forsaken content on my account (the same account under which it was purchased), both of our Xbox One consoles were showing the Forsaken content as not installed.
I went to the Destiny icon on my home screen, pressed the menu bottom, selected Manage Game & Add-Ons, installed all of the Forsaken-related items listed under Ready to Install.
I did this on both of our Xbox One consoles, and now family sharing works. My son, wife, and I can all access Forsaken content under our respective gamertags.
English