It was a fully unified country way before 1929, unless you are counting Alto Adige and Trieste as conditio sine qua non to have a fully unified Italy, which I wouldn't.
As for the Vatican situation, the Italian kingdom completely conquered and annexed the papal state in 1870 (Breccia di Porta Pia).
In 1929 the Pope formed an alliance with Mussolini to get a state in exchange for the approval of the fascist government from the Church (and other stuff, but that's the gist of it)