The Constitution does make provision for what you say ... it’s called “Impeachment” and then “Conviction”.
Of course we saw how that worked for Clinton in the Senate.
Are you saying that Congress cannot authorize the military to detain enemy combatants for the sake of national defense?
Bear in mind - I am not saying the military should remove Obama from the Presidency. I am saying that they are authorized to DETAIN him as an enemy combatant. Congress can decide what to do from there - whether to impeach him or not, but while he is detained he could not dispense the duties of the office and so the Constitutionally-authorized line of succession would come into play as to who is to ACT AS PRESIDENT, just as it would if he was shot like Reagan and temproarily (or permanently; that would be up to Congress) couldn’t perform the duties.