To be extremely concise, Jordan's independence in 1946 was challenged by the Jewish Agency based on the League of Nations 1922 decision which actually never set up a separate geo-political entity. It postponed the application of close Jewish settlement in the area east of the Jordan River
In the territories lying between the Jordan and the eastern boundary of Palestine as ultimately determined, the Mandatory shall be entitled, with the consent of the Council of the League of Nations, to postpone or withhold application of such provisions of this mandate as he may consider inapplicable to the existing local conditions, and to make such provision for the administration of the territories as he may consider suitable to those conditions,
but prohibited its dislocation from the Jewish National Home:
The Mandatory shall be responsible for seeing that no Palestine territory shall be ceded or leased to, or in any way placed under the control of the Government of any foreign Power.
The United States State Department agreed with the legal analysis.
So, I was surprised to read this account which eliminates the existence of Jews, Zionism and the Jewish National Home:
Status of the Emirate
According to the U.S. State Department Digest of International Law the status of the mandate was not altered by the agreement between the United Kingdom and the Emirate concluded on 20 February 1928 which recognized the existence of an independent government in Transjordan and defined and limited its powers. The ratifications were exchanged on 31 October 1929."
In 1937 the US Consul General at Jerusalem reported to the State Department that the Mufti refused the principle of partition and declined to consider it. The Consul said the Emir Abdullah urged acceptance on the ground that realities must be faced, but wanted modification of the proposed boundaries and Arab administrations in the neutral enclave. The Consul also noted that Nashashibi side-stepped the principle, but was willing to negotiate for favorable modifications.
Transjordan applied for membership of the United Nations on 26 June 1946. The Polish representative said that he did not object to the independence of Transjordan, but requested that the application be postponed for a year on the grounds that legal procedures required by the Covenant of the League of Nations had not been carried out. The British representative responded that the League of Nations had already approved the termination of the mandate in Transjordan. When the issue was voted on, Transjordan's application achieved the required total number of votes, but was vetoed by the Soviet Union which did not approve membership of any countries with which it did not have diplomatic relations. This problem and similar problems caused by vetoes of the memberships of Ireland, Portugal, Austria, Finland and Italy took several years and many votes to solve. Jordan was finally admitted to membership on 14 December 1955.