I think you are very wrong here. Every soldier is responsible for recognizing who his commanders are at all levels of command.
Just for a moment let's hypothesize that Obama is not eligible to be President or Commander-in-Chief. In such a hypothetical case, what obligation does a soldier have to obey his commands?
If you KNEW that Obama was not eligible to be President or Commander-in-Chief, what obligation would YOU have to obey his commands or to obey laws which he had signed?
I hate to break it to you, but there is no reason to believe Obama wasn’t born in the US with an American mother. You can debate if that is good enough, but it was good enough for the American people (who elected him), the US Congress, and the Supreme Court.
If the LTC doesn’t agree, he should have put in his papers when it became obvious Obama was going to be installed as President. But he’s been taking the Queen’s shilling, so now it is time to do her bidding - so to speak. He had the option of getting out, but CHOSE not to do so.
No sympathy for him from me. Sorry.