I'm not understanding your post??
I also work in education and am an 'essential user' so get a travel allowance.
Over a year ago, I stupidly drove my car on a flat (I didn't realise! I knew there was something wrong with the car, as there had been for a few days, and all I could think of was to get the bloody thing home before it conked out!) and it was unstable. I was reported as a suspected drink driver and breathalysed which proved that I wasn't. An officer suggested a 'deal' where I accepted points and a fine, and as I said at the time, I'd have been a dick not to take it.
However, he was overruled by a senior officer who insisted on taking it to court. I engaged a solicitor who was deeply unpleasant until he realised I was a middle class, well-educated professional, with a clear 40 year driving record, and I was hugely mortified about being in this position. He said he wasn't used to dealing with people who were devastated about what had happened!!
He represented me in court 3 times - I didn't have to attend TG - and my 'sentence' was commuted to doing a safe driving course - no points and no fine! I was, and am, hugely grateful!!
I didn't have to tell my employer - it was none of their business??