As an airplane junkie and aeronautical engineering student I can tell you I had a similar problem with my parents, although not that severe. Since I taught them what happens in the cockpit during the flight, what are the physics involved in flying and piloting basics including navigation procedures, etc. etc. they fear has disappeared. I have to admit that flying is pretty much unnatural and it doesn’t feel good when you don’t know what is happening / what are you feeling, but once you learn what’s behind scenes the confidence is extreme. F.e. my mother was extremelly afraid of that sensation of free fall you might have during a flight but when I explained her why that happened (vertical speed decrease or sudden downwards airflow pushing the aircraft as a whole) she started to lose panic. It then became bereable.
I appreciate your post. This might sound weird but it is not so much the mechanical part of flying that causes the attacks. My mom has worked for Continental Airlines my whole life and I have flown hundreds of times. I am not scared of being in a plane crash, it has a lot more to do with being trapped and knowing I cannot get out or pull over. Its basically panic attacks caused in fear of panic attacks and a slight agoraphobia.