They're fighting to be the ruler of Egypt! The story is a little confusing because of the amount of characters but I went through the family line photo and matched up the faces with the situation and it make more sense. Seth killed his brother Osiris and he came back from the dead during the trial however it seems like something is going on between Osiris and Seth (maybe forced sexual acts considering that Osiris tied Seth with vines)
Horus (the son of Osiris and Isis and Seth's nephew) is fighting for the throne to avenge his fathers death.