The Rabbi's teach that one kingship does not overlap with another even a hairbreadth (Yoma 38b). I understand this to mean that there may be only 1 Jewish king ruling at a time, or in the case where the Jewish people were divided, one king ruling per division at a time. However there are times in history such as the anointing of David or Yehu in which there were two people anointed as king at the same time.
I would like to know what the status of both the original and newer kings were during those time frames. For example would the concept of rebelling against a king apply equally to both of them - meaning if a person acted in a rebellious manner to either the original king or the new king would that be considered rebelling against the king? Another example would be the injunction against having too many wives or horses etc.