Nope, your at-will, can be fired without just cause and currently have a parent/child relationship with your management. Knowledge of this fact is evident on the faces of every CA, Flex and Avantiar pilot I see out on the road.
I survived five years of the at-will parent-child environment at Avantair. The secret: Do the job in a proactive, professional manner and stand your ground when issues arise that make it necessary to do so.
On the other side of the coin, I was fired from my previous job (my first ever union job after 40+ years in the work force) because the Captain screwed up and convinced me that he had straightened it out with the CP. Silly me. I believed him and failed to throw him under the bus. My Union, which had been collecting my dues via payroll deduction, didn't lift a finger and the steward who was "representing" me didn't say a word during the exit interview.
Forgive me if I'm not a big fan of unions.