But you are the head, it's obvious you aren't going to kill people but your incompetence might lead to it.
The bottom line is, and I have experienced this in my work, is that when you are #1, other people may mess up but it is ultimately YOU that carry the can. If you disagree or are incapable of understanding this, then get off the pot and let someone else have a go.
I can see why your last employer thought it was okay to unfairly dismiss you. You're a doormat and you expect others to be so too.
If this lady was at fault, then it would have been an open and shut disciplinary case, albeit one that may have dragged out for a few months, there'd have been no notice period, no compensation etc. Alternatively she may have just taken the easy route and resigned, collecting her notice period salary whilst on gardening leave. Either option would have been very easy to facilitate if appropriate, and both would have cost the tax payer considerably less.
If you want to aim your indignation at anyone, aim it at the idiotic Ed Balls. She has not been shown to have done anything wrong.