There are three different The Nuclear Option missions, one each for The Railroad, The Minutemen and The Brotherhood of Steel. Personally, I completed it with The Brotherhood, but it doesn't matter which faction you choose. The Nuclear Option will be the culmination of all other faction missions, and will likely result in you becoming enemies with the other three (Institute included). In completing the required quests for The Nuclear Option for both the Brotherhood and Railroad, I never had to fight Minutemen. I did not complete enough missions for them, but they do have a Nuclear Option finale.
This trophy is missable. Only Nuclear Family or The Nuclear Option are obtainable in a single playthrough, unless you revert back to prior saves.
If you want to complete all faction-specific quests and both ending trophies with as little effort as possible, I followed this guide over at PlayStation Trophies on exactly when to make separate saves.
http://www.playstationtrophies.org/forum/fallout-4-a/278938-...