I have trouble meditating on Our Lady being our mother and Our Father as actually father. I guess that's not really a convert problem but a family one. Born and grew up with non-catholic, narcissistic parents, I was treated like a tool and a burden not a person. I guess logically I can imagine about what it's like for Our Lady to be a mother to us but it's a hollow and distant concept to me and sometimes even triggering. I don't actually know what it's like to have loving parents so I can't make that good meditation of that. It also creates social problems for me because I live far away from my parents, people at church will ask questions like: "How are your parents? Are you going back to visit them soon? Do you miss them often? Do you talk on the phone often?" Due to me not wanting to expose faults of others I usually could only answer no not really without explaining why, and then I'll get this weird look and "well you should they must miss you very much" etc.
I have much compassion for you! I struggle with the same thing, my parents were self absorbed and abusive as well, very worldly and impure people too. I can relate to those situations you describe at Mass. It is a terrible feeling and isolating.
I would highly recommend some reading for you,
The Glories of Mary by St. Alphonsus Liguori, in which the saint writes extensively on the mercy and charity of Our Lady: https://archive.org/details/thegloriesofmary00liguuoft/page/n3/mode/2up
Holy Abandonment by Rev. Vital Lehodey is a beautiful book that describes how to view God as He is, how to find His will, and to see His loving hand in the events of our lives, and how to respond to Him as His child: https://archive.org/details/holy-abandonment-000001389
I hope and pray that should you choose to read these, it helps to redefine in your heart how a mother and father should be. I have had to do this and am still working on it.
There is also a book all about St. Joseph, which would help you see an earthly example of a most admirable man and father:
https://archive.org/details/lifegloriesofstj00thomuoft/lifegloriesofstj00thomuoft/page/n3/mode/2up