In OTL, before the war began, Israeli PM Levi Eshkol spoke to King Hussein on the phone, urging him to keep out of hostilities, should it come to that. Of course, Nasser of Egypt was twisting his arm hard the other way. Then, on the morning of June 5, 1967, Jordanian radar picked up a large group of aircraft which were approaching Israel from the west. The Egyptians claimed that this was their airforce, coming to wipe Israel out. In truth, the planes were Israeli, returning from just having destroyed the Egyptian air force on the ground. Believing what the Egyptians told him, the king made the fateful decision to go to war, and about 11 am, Jordanian shells began to crash into West Jerusalem. And the rest is history. Now what if Hussein had been a little more cautious, and wated to see how well the Egyptian 'raid' on Israel succeeded? He might then have thanked his lucky stars that he had been prudent.
OK, so otherwise, the war goes pretty much as in OTL. The 3 armoured divisions commanded by Gens. Tal, Yoffe and Sharon kick ass in Sinai, and are on the canal by the 8th, then the IDF goes north to do the Syrians in. Now some of Central Command's forces join in, because they are certain that Jordan will do nothing untoward. The attack goes off as planned, and the IDF stops 30 miles from Damascus, just as in OTL.
So now, what happens with the so called 'west bank'? When do the Palestinians and other Arabs start making noise about their state? Is the king going to be at all receptive to this, or will his response be whatever it was in the previous 19 years when Jordan controlled the west bank.
Millions of butterflies will come out of this. But lets assume that for the moment, Nasser continues to be bellicose, the War of Attrition still happens, and Nasser dies around the time he did in OTL, [Sept.- Oct. 1970] and is succeeded by Sadat. I can even see a Yom Kippur war still happening, but I imagine in this TL the events of September 1970 will be drastically different. If the King decides to put the west bank on a fast track toward independence, perhaps he can avoid all the trouble he had with the Palestinians in OTL. Does Arafat become the first Palestinian PM? Of course, poor Gaza is still out in the cold, because they are under Israeli occupation, and wouldn't be much better off if Egypt still ruled them.
I can see a much earlier peace treaty between Israel and Jordan here, with some sort of limited Israeli sovereignity over the wailing wall and the Jewish Quarter of the Old City. Undoubtedly the Palestinians would have East Jerusalem as their capital.
A curious bit of trivia: I can remember reading that life magazine in 1967, the one which showed the Israeli soldier swimming in the Suez Canal, and Life reported that 15, 000 Jordanians had been killed in the war. This figure was way too high, years later I read that 696 were killed. I always wondered where Life got their info from?