Sounds like the Director of Ops had it in for you and in a situation like that it doesn't matter if you're right or wrong. You made the mistake of getting on the bad side of the Director of Operations, gave him ammunition to use against you, and then made the tactical error of assuming that the big boss would stick up for you over his own D.O. That is bad office politics, you might win a few battles but in the end you make an enemy who has influence over your job. It might not be fair but that's the way it is at a lot of places, you might feel you did nothing wrong and maybe technically you didn't but perception is reality and sending your student off to do something while you "go have a smoke" sends all the wrong signals. Some places are stricter than others but the bottom line is you smoke on your own time, period. I've been in your situation before, (not fired but close to it) and I get the feeling from your post you're a lot like I was. Right now all your defense mechanisms are kicking in and it's a natural knee jerk reaction to be angry with them and hold yourself completely blameless, but in a few years after the initial sting of getting fired goes away and you've had some time to reflect you might feel differently about it.
P.S. No flight instructing job on this earth is worth suing over unless you can prove they sexually harrassed or somehow discriminated against you.
P.S. No flight instructing job on this earth is worth suing over unless you can prove they sexually harrassed or somehow discriminated against you.