The Jordanian constitution actually specifies royal succession by agnatic primogeniture, although the King is permitted to substitute his brother for his oldest son by an amendment passed in the 1960s. I don't believe most of the Gulf monarchies have written constitutions and, except for Bahrain, they don't even make a pretense of being constitutional monarchies. But in any case, I think they all allow the monarch to appoint whichever of prince he wishes as his heir. It's in many ways the ultimate check against the possibility of constitutional government. The absolute monarch has the power to pass on that absolute power to the person of his choice. And the choice usually seems to fall on a brother, imitating the old Ottoman tradition of passing the successions horizontally rather than vertically. (Although among the Ottomans it went to the next oldest prince. The Sultan did not have any discretion.)