Do you have links to this information? I have found some info on the private revelations related to it but not about St Pius X's rejection of it. Instead I read that he ratified the indulgences. Either way, it's still not what Our Lady asked at Fatima. I don't know why it seems so difficult to do exactly as she asked.
I was writing from memory last night, but I’ve now found the book,
The Sorrowful and Immaculate Heart of Mary: Revelations of Jesus and Mary to Berthe Petit - A Belgian Mystic (1870-1943), republished by the SSPX, London, 2002. It was written by a French missionary priest in the 1950’s or 60’s and the translation has a US imprimatur of 1965.
Perhaps St. Pius X wasn’t being exactly cold in his letter of 1911 to Cardinal Mercier, but he certainly wasn’t encouraging. The book says:
In a letter to the Belgian Primate written with his own hand, the Sovereign Pontiff said in conclusion: "Your Eminence had exercised the privilege of granting 100 days’ indulgence to the ejaculation. I would ask that the pious lady be content with this for the present."
It wasn’t Pius XI but Benedict XV who granted an indulgence to the invocation, but it’s not clear from the book whether it was a local or universal one. There is no prayer to the 'Sorrowful and Immaculate Heart' in the Raccolta of Indulgenced Prayers of 1951, so if it was universal, it must have been suppressed by then. The Blue Army didn’t consecrate themselves to it, they just 'adopted the invocation'. It does seem that this devotion sank without trace after Fatima and the spread of Reparation to the Immaculate Heart, except in a few small circles, and it certainly comes entirely from the Berthe Petit allocutions.
These can be criticised from both a religious and historical point of view, but it would take a long analysis. One example: in 1917, Cardinal Bourne of Westminster, who caught Cardinal Mercier’s enthusiasm, consecrated England and the British Empire to the Sorrowful and Immaculate Heart of Mary. The voice attributes the Allied victory in WWI almost entirely to his actions. On October 17th, 1918:
Had I not intervened in answer to recourse to the Sorrowful and Immaculate Heart of My Mother, and through the leading of My apostle Francis [Bourne], victory would have been on the side of [Germany and Austria].
So Our Lady is made responsible for the Balfour Declaration? And the banishment of Emperor Charles and the destruction of the Austro-Hungarian Empire, to which the Church had transferred the prerogatives of the Holy Roman Empire? Etc.
One more quote, from the Second World War, Nov. 1941, with the Germans still the absolute villains and no mention of Russia:
The chastisement is rumbling, the leaders [of Germany] feel it coming near, they dread it and they realize that they can do nothing to avert it. It is then that My judgment and the power of My Will shall be made known. My Work will never fall short of achievement. Belgium will again be prosperous. (My italics)
I can’t believe this is Our Lord speaking!
Could the whole thing be a fαℓѕє fℓαg by the Enemy to distract from Fatima?