Is it permissible for the regular Imam to establish another congregational prayer while a divergent congregational prayer is being held in the mihrab and he is present, or should he wait for them to finish?

No one has the right to lead people in prayer when the regular Imam is present, because he has a greater right to lead. It has been forbidden to lead a man in prayer in the domain of another. The prayer led by the regular Imam in his mosque is like that of the master of the house. Therefore, if the regular Imam is present, no one is permitted to take his place, unless he is delayed in a way that causes hardship for the worshippers to wait, or due to an excuse. The prayer established without the permission of the regular Imam is invalid or disliked, and worshippers are not permitted to join it. The regular Imam should not establish another prayer at the same time to avoid confusion. Rather, he should wait for the dissenting congregation to finish, then establish his prayer, and admonish them for their error.