Lathyrus
With no contract and never having actually worked there it wasn’t really a job, so you don’t have to put it in your CV. Like Forsythia says just leave a gap.
If anyone asks about the gap say you did accept a post but they were unable to provide you with the training needed. Make it a positive for next employers, you’re keen to the job well and looking for a company that values their employees.
Very good points in your post Lathyrus. If you were to work with vulnerable children and something go wrong, the situation would be far worse. Sticking to your guns is a sign of strength, not weakness. You are on the right path.