Does her new employer think they have dismissed her? My understanding is that, in most circumstances, a fair dismissal has to include a written statement of the reasons for the dismissal and a right to appeal against the decision. Has she been given these? If not, take the matter up with ACAS.
I find it difficult to believe that ANY teacher thinks it makes sense not to be a member of a trade union. There are, after all, plenty to choose from in the teaching profession.
Just as an example of one reason for belonging to a union ... How does she imagine that she might defend herself...