Jim, I really feel for you. The thing is, people, some people, simply have no character. It's almost as if they have no soul. I've sat across a table from two men who were respected and generally liked - indeed, that included me until I was shown the truth. They lied, and lied, and lied. Not very serious things, but as they put it, added together it made it questionable that I should hold my position in a demanding job.
What they cited was contrived and bewildering. Bewildering, because they were saying things that were bordering on Pythonesque. At that time, I didn't need them or that job, but hell, I wish I'd fought them on principle.
All this is about people. I have no idea why I didn't fight back then, but you need to - need to both for the result and how you will feel if you don't.
Just know you are not alone, and for hell's sake don't do what I did and take the line of least resistance. Fight. And let them know you're going to fight until your last breath. It may sound over dramatic, but people like this just don't care about others and how much they hurt their staff - and indeed the families of staff they have a moral if not legal responsibility for. Expect no decency from them. Their character is flawed and no amount of reasoned pleading for fairness will do a jot of good. But you have one thing going for you: these pathetic examples of human beings will so often buckle when in a real battle. Fight to win, and for the moment at least, don't allow the fear of losing to dampen your resolve.