"By Dawn's Early Light" is a movie with James Earl Jones as "Alice" the general aboard an EC-135 carrying out the "Looking Glass" mission (a 24/7 airborne command and control, now obsoleted) after a surprise attack. Jones' character decides to ram Air Force One to eliminate the hawkish Secretary of the Interior who has assumed the role of President - and thus resolve a deadlock so that the actual President (who has survived, badly wounded and unable to prove his identity to those aboard Air Force One) can countermand US forces and prevent a retaliatory strike which would inevitably cause World War III.
It's made for TV but I thought it did a surprisingly good job. I don't know whether you actually could chase and collide with the plane normally designated Air Force One in an EC-135, but certainly I'd bet on military pilots to give it their best shot if their commander explained the consequences otherwise.