Tiger Lily,
I once listened to a Baptist gentleman describe to me an apparition he had had. He said it was an angel that appeared to him; had he been Catholic, quite likely he would have said that Mary had appeared to him.
I draw a distinction between approved apparitions (and that is perhaps the word that you are looking for), unapproved apparitions, and “apparitions” that have been declared false. Lourdes, Fatima, and Guadeloupe have been approved: the Church has thoroughly investigated what happened and has concluded that most likely it was the Virgin Mary who appeared to the visionaries. By far most apparitions are unapproved, meaning that the Church simply has not looked into them yet. (With many apparitions, the Church will never look into them; the person for whom the message was intended will receive the grace, everybody concerned will get on with his life, and nobody will think much about it any more.) “Apparitions” that have been condemned, such as one to a supposed visionary in Denver a decade or two ago, did not involve Mary at all but were either demonic or involved only the imaginings of the supposed visionary.
The statement that “Mary appears because Jesus cannot” is incorrect. (I realize you phrased it as a question; I am just trying to speak clearly.) Jesus has appeared to many visionaries such as St. Faustina.
I agree with you totally, Mary is the “ultimate mum.”