The Hashemite Kingdom of Jordan could not survive the creation of a Palestinian State. Israel could, perfectly easily and indeed rather well. But the Hashemite Kingdom of Jordan could not.
There is nothing historic about stopping at the state at the river; just read the Bible with a map to hand. That was why the West Bank was in Jordan. Most of the population is still on the East Bank, and is Palestinian accordingly.
So the ruling house and the Bedouin elite around it would be told to back its bags and clear off back to the Peninsula. The East and West Banks would be reunited, the former bringing the Jordanian desert with it.
And the water problem would be solved.