Any aggrieved person can file a complaint (FIR) as and where he/she feels comfortable. It the duty of the receiving official/policeman to transfer the case to the correct police-station.
In your case, it is quintessential to first read the filed complaint. If all the allegations as per the complaint belong to city-1 then there is no case made out at city-3 and such FIR can be quashed per se. However subsequently another FIR in city-1 shall be lodged automatically.
For further explaining your query, if your wife has been successful in getting the complaint registered in city-1 and you have the copy of this FIR, then you have to move to High Court of that state and pray to quash this FIR and get the case transferred in the correct area o jurisdiction.