There was much debate about this subject at a RC forum I sometimes frequent, just in general not the actual apparition itself. Personally, I do not believe it (I never think about RC apparitions anyway) and it makes me wonder why any Orthodox would. She does not sound like the Theotokos we see in St. Luke's Gospel at the Annunciation or at the Wedding of Cana. I did appreciate the post from blackincense, however. I do believe, if it is indeed a false apparition, God can still bring good from it. That's not been my experience. I have been Catholic since 2007 and I have never once heard the Marian apparitions brought up at Mass. If they are really so important to us as you say then I would think I would have heard them referenced in a homily by now.
From my experience, however, RCs put A LOT of stock in their apparitions. The official teaching from what I recall is that the faithful can be agnostic to them, but Lord help you if you as a RC say you don't believe in Fatima, Lourdes or any other Marian apparition!
I was a Catholic for 34 years and have been to countless Masses in dozens of states and in two countries (well, one, really, but Quebec really is like being in another country). I can count on one hand how many times Confession was referenced in a homily, even during Lent, from the time I was able to understand what the priest was saying until present. I can say this with conviction because I'm one of the few people who actually likes listening to priests give homilies (even boring ones) and I happen to believe that Confession is not preached enough so my ears perk up on the incredibly rare times I've heard it.
I can, however, tell you about the one priest who preached the importance of Fatima in every
single sermon he ever gave, or at least the ninety or so sermons I heard him give between 2000 and 2003 when I attended his church.
Please be aware that I agree with you that it's not technically required
for Catholics to believe in private revelations, but its pretty hard to not think that, for all practical
purposes, belief in approved apparitions is not just approved but encouraged.