James, I can appreciate that your family and yourself were tired and ready to get home. At the same time, I suspect that you approached this situation (whatever the rights and wrongs) in a manner that was bound to end in tears. Nobody reacts well to a raised voice as a starting point and that then sets the tone for the way in which the conversation develops.
Had you approached this issue rather more gently, I suspect you’d have got a lot more by way of explanation and sympathy. By the sound of things, this was a ground staff problem in that they boarded you early, before the crew were ready. After all, all of us, including air crew, are entitled to a break during a working shift.
Maybe you should also think about the example you are setting for your 12 and 9 year olds who may now see raised voices and agressive behavour as the norm when relating to service staff in the future.
Sorry to be so blunt but its difficult to have too much sympathy for you in the circumstances you describe.