What about the thread going on where the Holocaust is less bloody and their are more surviving Jews to move into the region around the time of the War of Independence? Could that be a reasonable way to have Israel gain all of Jerusalem early on?
Besides the oxymoronic obsurdity of defining a "less bloody Holocause," perhaps a less thorough and industrialized one, even if a large part of it was carried out like a gigantic progrom in the east where Nazis didn't have the "luxury" to build such facilities for mass killing nor the rail networks to get many there. It would have to be as horrific to those who survived in order to have such a strong resolve to make their nation while taking part in what ultimately was a 20 year war of attrition (1948-1967) with enemies on all sides.
You also have to consider that Jordan had the best trained and equipped army at the time of all Arab states armed with (sans-jetplanes) the best Britian can provide. The Haganah, Irgun and other Zionist resistence were already in a squeeze making sure as much of the people in fighting shape were armed and properly equipped with ammunition as is, it would not be as simple as having more boots.
The only two ways I see it is if Zionists had stronger international support from the start or Jordan was as ill-trained and/or equipped like its other allies. Also Ben Gurion and the crew realized due to King Hussein's relations with the UK and the rest of the West he was somebody they could more apply negotiate with for an armistice then the other militarist and monarchal dingbats. It was just too much of a risk for the state's survival itself to forfeit.