I have good and bad news. The bad news is that the state's treatment of you is unlikely to constitute an unfair labor practice under the National Labor Relations Act, since that pertains to union organizing and activities and not individual decisions. The good news is that your union should have a grievance procedure that you can go through with a representative in order to work out an agreement and get you reassigned. If the employer were to refuse and this constituted a breach of the contract between the Department and your union, then the union could file an unfair labor practice, but that would still be unlikely to help you in the immediate future.

Another option is to file suit against your employer for failing to provide you with a reasonable accomodation, which is allowed for in your bargaining agreement and was decided by the arbitrator. If the arbitrator's ruling is unclear (which is what the company is likely to argue), then you would have to bring suit in order to get the arbitration agreement enforced. The good thing is that you should have employment protection from your union and that they should have procedures in place to put you in another similar position. I would ask your representative to contact your employer to reinform them of their obligations under the collective bargaining unit, and that their failure to comply with the arbitrator's ruling would constitute a breach of your employment agreement, the collective bargaining agreement, and the union's collective bargaining unit. I would try going through this procedure and seeing if the union can either obtain you the transfer request to which you're entitled, and if not, if they're willing to file suit against the employer on your behalf, assuming the employer's actions of not accomodating you are in violation of the terms of the collective bargaining agreement, which they most likely are. If neither of these options are successful, I would consider hiring an employment attorney, but only on a contingency basis, so you don't have to pay him anything until you collect from your employer. Additionally, your collective bargaining agreement should provide you with protection against being discriminated against for filing a complaint or trying to get the arbitrator's decision enforced, and if the employer fails to comply with it they can be found to be in breach of contract and to have violated the collective bargaining agreement. Also, again, you would first want to go through your union's representative before getting your own legal representation to minimize costs. I hope this information is helpful. It definitely seems like an extremely trying ordeal. Good luck with everything.

It's odd, but the person who doesn't breach the contract is still supossed to mitigate the damages. In your case, getting another job, so making you whole is only to give you that difference but PLUS the expenses you incurred in obtaining your back pay, since you would not have had to make them had the wrongful termination not occured. (E.g., payments for legal advice, paperwork, etc.)