What should a person do if injustice befalls him or he has a dispute with another, and he has no option but to resort to Bedouin tribal arbitration (Haqq Arab) or state judiciary, both of which rule by other than what Allah has revealed? And should he remain silent about the injustice, or should he resort to these man-made laws in an effort to claim his right and remove the injustice from him?

There is no blame upon you for resorting to man-made laws if you find no legitimate Islamic means to reclaim your right and remove injustice from yourself, provided you detest them and disavow yourself of them. The alternative to this would be for the oppressor to increase in tyranny, for rights to be lost, and for corruption to proliferate. Al-Izz ibn Abd al-Salam mentioned the permissibility of enforcing the rulings of disbelievers if it leads to securing public interests and repelling widespread corruption.