"He was giving His mother to all of us as well."
I'm not catholic. But from the outside looking in, I was always led to see the rc church itself as the 'mother' .... while Mary was someone to pray to.
In other words, I've never heard of any catholics leaning on the "mom" aspects that Mary represents. Rather, I've thought the focus was that she was an intercessor.
From inside (though only recently), at least in our parish, the Church is the body of all believers, of which Christ is the Head and King. Mary is the mother of the King, and thus the archetype of mothers.