Article I, Section 8 gives Congress the authority to make laws necessary for executing Constitutional powers. One of those laws says that in carrying out the 12th Amendment (which you cited) the VP has to ask if there are any objections to the electoral vote count. Dick Cheney never did that. The law for certifying the winner of the electoral vote was not fulfilled. Without that step being lawfully done, nobody CAN be lawfully inaugurated.
Obama can no more be the Commander-in-Chief right now than I can. I have as many *legal* qualifications as he does at this point, PLUS I have a legally-valid birth certificate to prove my age, parentage, and place of birth. The only legally-valid BC Obama has is from some place besides Hawaii, because his Hawaii BC is not legally valid; it’s been amended and almost certainly was also late - both things disqualifying it from being legally probative.
IOW, we know that he has not been lawfully certified as the electoral winner, and we know that he has not been lawfully certified as eligible for the office of POTUS. The entire legal procedure has been evaded.
Is that problematic for you?