Moving forward, how would Italy's relationship with the Papacy fair without a fascist regime in control? How would King Victor Emmanuel III (if he's still in power) be viewed by the people and the popes in the Vatican?
I can probably give some insight to this.
First, we must understand the Real-Life relationship with the Papacy and the Italian government during that time. I will only give moderate details because both Catholic and Italian history is too big to digest in one post.
After the Fall of the Papal States and despite assurances from the Kingdom of Italy that the pope is independent, there was major distrust from Pius IX-Pius XI. Reading the Law of Guarantees, Pius IX concluded that the idea of a completely independent pope was uncertain. Anyway, throughout the rest of the 19th Cent. all the way up to the early 20th Cent., the popes refused to recognize Italy and took great care to not grant any motion or word to its legitimacy. When Mussolini comes into the picture with his Fascist ideology, he wanted as much support from the Italian populace as possible. Despite his irreligious views and his active anti-theistic/anti-Catholic personality, he wanted to win the support of Catholics and set up a façade that he wanted the Italian government to reconcile with the Holy See. Pius XI, at the time, also wanted an end to the "Roman Question" and sent his representative to create an official treaty. Mussolini represented Victor Emmanuel III and they came up with the Lateran Treaty on Feb. 11, 1929, giving birth to Vatican City State.
Assuming that Italy does not get involved in the First Great War (an extremely unlikely scenario that I will never stop saying...), I suppose that Pius XI would still want to seek a reconciliation with the Italian government, given that it was one of the reasons why he chose the name Pius. It all depends on whoever is the prime minster during his reign. Would he have been another anti-clerical prime minister who would have kept the
status quo or someone who also wanted to see the beginning of new relations with the Holy See?
If it's an unsympathetic prime minister, then there would still be no diplomatic relations between Italy and the Papacy. It would probably remain so until after the Second Great War.
If it's a sympathetic prime minister, then it would more or less end with the same results that the Lateran Treaty says. Same treaty, different names/people.
I am inclined to go with the former, perhaps to give some variation to TL-191, even though I would like to see the Papacy gain its independence back. Now, a question that I do have is if a hypothetical papal state that is created in TL-191 would have different borders: Leonine City or Vatican City?
Source:
https://www.alternatehistory.com/forum/threads/the-popes-in-leonine-city.304121/#post-8638361
Victor Emmanuel would probably not lose the support of Italian citizens as it did in OTL and the monarchy would still be popular without the rise of Fascism. He probably would still make the same mistakes with Ethiopia and Albania. The popes would still pray for the King of Italy and hope that he would agree to seek reconciliation with them.
Historical Sources:
https://en.wikipedia.org/wiki/Leonine_City
https://en.wikipedia.org/wiki/1922_papal_conclave#Blessing
https://en.wikipedia.org/wiki/Prisoner_in_the_Vatican
https://en.wikipedia.org/wiki/Lateran_Treaty
https://en.wikipedia.org/wiki/Benito_Mussolini#Religious_views
https://en.wikipedia.org/wiki/Victor_Emmanuel_III_of_Italy#Loss_of_popular_support (Just read the entire article for a complete understanding of how he is/was viewed)