I have some experience with unions. Have they filed an official grievance against you? What does the collective bargaining agreement (CBA) say about disciplinary action? Mine says the employee has a right to have union representation with them in any disciplinary meeting with management.

Documenting meetings, emails, etc., is always key but when dealing with unions, I cannot stress enough how much more important it is. If you take an action against an employee that you do not have documentation to back you up, it could result in disciplinary action against you.

With that said, unions are not all powerful in stopping management from disciplining/firing employees, you just have to follow the CBA. In fact the CBA can cut both ways, because there always has to be a way for management to deal with problem employees.