First thing to say is she hasn't been sacked. She has been suspended during an investigation into an incident or series of incidents. She has not been sacked, or given any kind of warning either.
It's difficult to advise on what appropriate action would be for the employer to take should they decide after the investigation that her use of the email facility was inappropriate, as there's not enough information to tell. But at the moment they've not taken any disciplinary action anyway.
Suspension pending an investigation is not disciplinary action, it's removing someone from the workplace while an employer looks into a situation, gets the facts together and decide whether or not disciplinary action is appropriate or not. For all you know they may have been on the verge of deciding not to pursue it at all, or to give a verbal warning or something.
Why on earth did the union rep advise her to resign? That's bizarre! The only reason I can possibly think of is if she had definitely done something so bad that she was bound to be dismissed and she decided she wanted to resign beforehand so that her reason for leaving was not dismissal. I can't think of any other reason why a union rep would advise someone being investigated to resign. Oh, except if it was something very sensitive they'd done that they didn't want coming out publicly and preferred to just walk away quietly, I've had that before.
Don't really feel I can help more at the moment tbh, perhaps you'll have more information soon. But if she has resigned during an investigation and regrets it, it's difficult to see what she could do tbh. Her employer has done nothing wrong that I can see, not yet at least. Any claim would be against the rep for bad advice.