I don't know if it was militarily possible, but suppose that Israel had captured East Jerusalem from the Jordanians during the 1948-49 war. Would an undivided Jerusalem, within the 1949 borders, have more international legitimacy as Israel's capital?
Likewise, what would this do for future conflicts in the area? OTL, even without the Israelis having the eastern part of the city until 1967, there was plenty of hostility and clashes. If there is a Suez Crisis in this ATL, might Jordan intervene on the side of Egypt in order to get back what they lost? King Hussein would probably not be eager for a rematch, but he might feel pressured to act.