If one believes that the Beis Din didn’t act properly in a din torah, and the Beis Din has given its decision, what are the person’s options?
This is a difficult situation. Provided the first Beis Din had proper jurisdiction and the procedure was not flawed (primarily, that the parties signed their names on an artibration document), another Beis Din is not authorized to take on the case, after the first Beis Din has already given a ruling. The best course of action is probably to write a letter to the Beis Din (or, preferably, to ask a dayan or to’en to write a letter on your behalf), explaining why you think the decision is wrong, and asking for a reassessment of the case.
If this does not help, the next option would depend on how grave a mistake, if at all, the original Beis Din made. A dayan or competent authority would need to be consulted about the particulars of the case.