The most consequential recipient of said orders is going to be a ballistic nuclear submarine deep underwater, and water is a terrific shield for the higher frequency radio bands a satellite will have access to. I'm guessing the command rocket will spool out an extremely long wire on its flight trajectory and give access to the VLF or ULF radio bands that can penetrate the ocean.

I think the command signal is merely picked up by existing repeaters that broadcast to the submarines.

I actually think the most consequential recipients are actually the land based ICBMs as those are likely 100% automated installations.

Even if the submarines are already at launch depth I would assume there would still be final humans in the loop in all nuclear bombers and subs, making them unreliable launchers. (who really wants to press the "end the world" button?)

I actually wouldn't be surprised if it did have a direct VLF antenna system. If the Dead Hand had triggered, that suggests multiple Soviet C&C headquarters went offline due to a first strike, and at that point you can't really assume your repeaters or silos are still online. The submarine fleet's primary purpose is to be the surviving second strike capacity.

Both the US and Russia have flying command systems which use very long trailing wires to send launch commands.

The problem: they're nearly a single point of failure. If you can hit the other side's command systems their missiles won't be going anywhere.

I'd assume both sides know this and contingencies and redundancies exist.

Easier to defend than a satellite maybe?

Correct. Also there is apparently multiple of them.

Rocket silos are incredibly difficult to destroy, even with nukes.

Anti satellite missiles would likely be the first things fired in WW3