'The truth of the matter was Queen Sophie did not like Elisabetta one bit and didn't help her with her new family.'
Perhaps it wasn't surprising that Sophie didn't like Elizabeth. According to biographies of the playwright Terence Rattigan, Elizabeth became pregnant by Rattigan's diplomat father, and had an abortion (see Oxford DNB entry for Terence Rattigan). I haven't managed to pin down a date as yet, but if this happened at the time Rattigan pere was required to resign from the Diplomatic Service in 1922, she was already married to George but not married for very long, and if earlier, before she was married and presumably before they were engaged.
Ann