It has taken some time but I have good news.
A lawyer contacted Southeastern advising that he would defend my daughter in court applying for dismissal and indemnity costs if they persisted. He referred them to their own 'making rail accessible for older and disabled persons' policy - specifically to a section on penalty fares; evidence that the fare had been paid; and that they had failed to follow their complaints procedure as indicated in their own transcripts of the recorded telephone calls.
Finally, he pointed out that as she had evidenced the paid fare pursuing prosecution was not in the public interest.
Southeastern withdrew. They did not, however, confirm this in writing to my daughter until a month after the court date which caused her further distress.
However, it's over, no criminal conviction, her DBS remains clear and she need not worry about her employment now.