Front doors won't open back doors will.

There is a trim piece that runs along the top edge of the door. It runs from the very top back of the door (over the window), along the top and down the leading edge. It slides backwards over time. Take a hammer and a piece of wood and tap it forward again.

Take a close look at the door as you try to close it and you will see how it is hitting on the B pillar.

I am trying to picture what you are saying and I cannot recall any trim piece like you describe,

Go take a look at the car. If yours if different than my old Regal we'll have to think about other things.