SK1NT you have probably already read this but just in case:
https://www.gov.uk/work-reference
You are right to pursue proof of other positive references given to agencies. The more of these there are and the more recently they were provided further undermines the later bad reference. It would...
If she got her second job with a reference from the school she resigned from it suggests it was not negative and that therefore the reference provided from the same school for her third post 5 years later was quite different - was it signed off by a different individual at the school? This could...