To "rise up over" something is an idiom that means to control it. Alternate translation: "taken complete control over his father's kingdom" (See: [[rc://en/ta/man/jit/figs-idiom]])
Jehoram probably did not kill them personally, but had other people do it for him. Alternate translation: "he caused all of his younger brothers to be killed" (See: [[rc://en/ta/man/jit/figs-metonymy]])