Um, no. Not even close. The only part you got right is that most of the present inhabitants of Jordan are of the same ethnicity as those in the territories.
The king of Jordan is not related to the king of Saudi Arabia. "Saudi" refers to the House of Saud, a particular dynasty from a particular tribe. The king of Jordan is not from that house, but is instead a descendent of King Faisal, who led the Arab revolt against the Turks in WW I. With a certain well-known Lawrence as one of the liason officers sent to work with him.
The UN did not exist when either of these lines gained control of their respective countries. The king of Jordan (just created as a seperate country) was seated by the British, as a reward for his services in the war against the Turks. Three other princes from the same royal line, Faisal's, were placed on the thrones of the new states of Iraq, Syria, and Arabia. None remain, except the line that received Jordan for its inheritance.
The House of Saud overthrew the one in Arabia, before WW II. The French deposed the one in Syria, also before WW II - they received Syria and Lebanon as their protectorates after WW I, as Britain's ally, but did not favor monarchy. In both Syria and Iraq there were revolts during WW II in which locals sided with the Germans, but the British put down both. Later, in the post war period (and after a spell of union with Egypt) the Baath party took power in Syria and installed Assad as tyrant. The king in Iraq was deposed after WW II by the Baath party, where Saddam rose through the secret police and eventually made himself the absolute ruler.
The House of Faisal was given most of the territory of the Middle East by the British. Only Jordan remains. The UN had nothing to do with it, and the king of Jordan is not a Saudi.