The Last Glorious Moment for Catholic Spain, and may I add for the West in general, occurred in the period of 1936-39, when for the last time Catholicism triumphed in arms against the forces of evil.
Many had a hand in that victory. Not mentioning heavenly aid, in the temporal sphere so many brave Spaniards endured a cruel war engaged by a cruel enemy. Their entire kingdom-- their entire way of life-- was at stake. The enemy was strong and looked invincible. It wasn't, thanks to the sacrifices and bravery of many.
Some had a more pure motivation; perhaps the Carlists, fighting explicitly for God and King. Some had a more noble pedigree, like Javier I. But what is undeniable is that, for all of the good and bad about him, the man who organized, motivated, directed and managed the cause to victory was General Francisco Franco.
The nationalist coalition beat the forces of international communism; there is no easier way to say it than that. That the victors of the war on sanity make us hesitant or ashamed to say it is proof of the near totality of their power now. Yet, in the late 1930s, in one corner of the world, they were stopped. It almost gives one hope, though we know that any such victory today would need a miracle.
Gary Potter at Catholicism.org has written a thoughtful piece on the effect of Franco's rule from 1936 to 1975 on the culture of Spain. He compares it to the Spain of today, and though it might spoil it for you, he finds it greatly superior. I agree with him. Because Franco ruled in such a way as to institutionalize the aims for which they fought.
My wife and I have traveled to Spain three times, first in 1998 (twenty-three years after Franco's death) and last in 2014 (nearly forty years after). While I can't speak to conditions during his rule, I can personally attest to a shocking and marked deterioration of the kind of issues Potter covers in the sixteen years between our first and last visit.
Excerpts are below. I encourage you to read it all; Potter links to an earlier piece he wrote on the Spanish Civil War, which is quite informative. If you are interested in this event at all, I also recommend Warren Carroll's The Last Crusade.