Can an officer or senior enlisted (not an MP) order or demand a soldier/servicemember out of a POV on post whilst driving?

If you're in this situation, drive to the MP station or public area before you stop.
I would expect rode rage more likely than an on the spot correction of your driving.

General Military Authority. If said Officer or NCO witnesses an unsafe act...such as driving crazy like....yes, they can order them out of the car and detain them until MPs arrive.

What was the driver doing or not doing while in the car? Disobeying a direct or a lawful order can bring you much more grief that stoping then complaining to appropriate authorities later. Driving on post is not a right and can be curtailed. If the other driver was road raging a quick call to DOD/MP HQ can fix the issue quicker and with less to no repercussions to you.