Army Regulation 600-20, Army Command Policy, governs chain of command.
Your contention “If Obama is not eligible, the whole chain of command is corrupted” is not supportable. Perhaps you should consult the Deputy Chief of Staff, G–1 who is the designated proponent.
The President is the CiC. He authorizes the use of the military. If he is not legitimately the President, he cannot command them. In the oath, they have to swaear to obey the orders of the CiC. If he is not legitimately the President, they cannot in good faith swear to follow his orders as they also swear to uphold the Constitution.
Is this what you are tallking about?
AR 600–20
Army Command Policy
This rapid action revision, dated 30 November 2009—
o Provides policy guidance for the legality of the Family Care Plan (para 5-5).
o Establishes policy on unit memorial ceremonies and services (para 5-14).
o Establishes DA Form 7666 for parental consent.
o Establishes DA Form 7667 for Family care plan preliminary screening.
o Makes additional rapid action revision changes (chaps 2 and 5).