Sounds like a nightmare boss. Firstly, the incident last year is not 'on her record', she was found innocent and received an apology, there was no formal warning or anything, so that definitely can't be used against her.
The recent incident, when you say "her new boss has taken it upon herself to say that it was my aunt and has officially recorded this", in what sense is it recorded? Was there a disciplinary procedure? Unless there was and a formal warning was issued, again that's not 'on her record' anyway. And the 'one more and you're out' thing is rubbish as well.
It sounds as though your aunt's boss has got it in for her for one reason or another, is ignorant of proper procedures and is trying to intimidate your aunt.
As she works for the council she will be protected by some quite stringent procedures and is in no danger of being sacked or anything like that, so there's no need to worry about that immediately.
As you say, she has paid an awful lot of money to the union so the first step is to make them work for it. Her rep is useless so she needs to go above his head. The union rep will have a supervisor and a head office and probably a complaints procedure as well. If your aunt knows or can find out the supervisor, that's the first place to start, but the head office of the union is also somewhere to go. Once she's got the union doing something for their money, they should be able to provide reassurance about procedures where your aunt works and hopefully advise her how to deal with her boss. A formal grievance is the obvious route but it's something to consider carefully especially when it's about her line manager.
I would also recommend she speaks to someone in HR in confidence as well. Again they will be able to advise her of how she can deal with the problems she's been having, and reassure her about procedures in place to protect her. It may be that lots of other people have concerns about your aunt's boss and someone needs to be aware of what's happening.
Something else she should do is get hold of the disciplinary procedure and grievance procedure. She will see from those that her boss can't sack her and that there is a mechanism for ensuring disciplinary issues are dealt with fairly, giving the employees the right to representation and appeal. Knowledge is power and that should make her feel a bit more secure hopefully.