That premise is that military flying belongs to AAWH and they can assign it to whomever they choose.
When Atlas bought Polar didn't they take over the Polar contract? Don't you expect them to abide by that contract? Isn't that contract then considered theirs to do with as they wish - as well as all the Pilots, Routes and authorities. Why do you say it is an Atlas Pilots premise? Isn't it just the way business is done? Atlas bought Polar so they can do as they want with the contracts and aircraft. Did you complain when the holding company transferred a bunch of aircraft to Polar? The answer to the title of this thread is of course Atlas actions will affect Polar as well. It is the same company with two different business units. Anything the holding company has done or will do to Atlas, they will do or have done to Polar.