www.bloomberg.com/politics/graphics/2016-nuclear-weapon-launch/
Above is the 'launch sequence'. Although it says that the Pres has final authority, note that the senior officer in the war room (usually the SoD) must authenticate the command. The war room also prepares the launch order. There's your 'fail safe'. Either of these two entities can stymie a launch long enough to remove an unstable president.
Reality isn't Dr Strangelove or a rogue president firing an order directly to some low level soldier to hit the button or a crazy general riding a nuke to perdition. Reality is that if the war room people (all high ranking military and the SoD) truly feel that a President is off his rocker and that a nuke launch would be a huge mistake, they can refuse to do their part in the launch. And I truly do believe they would refuse. They have just as much to lose as we do when it comes to MAD.
Article 25 Section 4 of our Constitution provides for the removal of an unstable or unfit president. It's a relatively simple process whereby the Vice President and Senior Officials convey to the Speaker of the House and Pres of the Senate that the President is unfit for duty.
www.law.cornell.edu/constitution/amendmentxxv
catgirl I'd be happy to move in and read you the nuclear launch sequence with emphasis on the fail safes and Article 25 every night before bed. But the bed would be a bit crowded with you, me, my DH, and our highly suspicious Dachshund. Not to mention your family!
I live on the US West Coast relatively near two prime targets. For one, I'd be obliterated. For the other I'd be in that nasty 'too sick to live, not sick enough to die' fallout area. I'm not worried one bit.
I'm working hard to get Trump out of office and/or to make him unre-electable. But that's because of what he's doing to my country and my fellow citizens (and immigrants) due to his domestic policies. Not because I'm afraid of nuclear annihilation.