You cannot come in the doors and windows are rigged with C4 to stop you... Yet the front door of the White House was blown off and remains a gaping hole the entire movie... Like they could not send in a couple hundred marines to secure the place.
Like you really could withdraw US forces from S. Korea in a few hours...
If I were the acting President, l would have simply said I am the President now, the US does not negotiate with terrorists, I do not care if you kill the President, you are not leaving that bunker alive.
Also if I were the general guy I would have ignored the order to give up my code. After all he was not the CiC any more, he was just another hostage and cannot give orders.