I’m Anglican and can help sort some of this out for you.
Atonement left the Episcopal Church to become Roman Catholic,they were placed under the authority of the bishop in the diocese where they reside. The AU were the first wave to go to Rome.Their liturgy is from The Book of Divine Worship.
The second wave went to Rome under the Pope’s personal ordinariate and are governed by a bishop who reports to the Pope.
Atonement wanted to transfer to the Ordinariate but for reasons unclear the bishop they were under nixed it and removed the priest. The congregation is upset because while they have grown they came in as an Anglican Use parish with expectations of remaining thus. There is property involved including a school that the diocesan may not want to lose if the church were to go to the ordinariate.
The other churches and organizations on your list are Anglican and have no relation to the Roman Catholic church. I can sort that out for you too if you’d like but they have no bearing on this story.
Thanks. Your post was most helpful.