Is there any circumstance in which a legitimate annulment can be obtained without filing any paperwork with the diocese and without the former spouse being officially notified?

My father was unfaithful to my mother over many years and had several children with his mistress. My parents eventually divorced because my father wouldn't stop seeing this woman. While this was going on, my dad stopped going to Communion. He obviously knew what he was doing was wrong, but didn't stop.

My father moved to another state with his other family. My mom refused to move us with him when she found out the mistress was moving also. He attended church and sent the kids to Catholic school, while still married to my mother. He would visit our family about once a month. This went on for some years.

Some time after my parents finally divorced, my father married the mistress. His priest told him there was some special circumstance in which he was able to give him an annulment without going through the normal procedure. I don't know how much of the true story my father may or may not have given to this priest or what this special circumstance could've been. The priest married my father in a private ceremony in his church.

I assume my father does not have an annulment. There was definitely no paperwork filed. If this is so, what is my responsibility as far as reporting this abuse? A Catholic counselor I know has told me that either my mom or I should report this priest to the bishop. Also, would it be right to tell my father he doesn't have an annulment or should I keep my mouth shut? I don't know whether he thinks he has a real annulment or if deep down, he knows the truth but doesn't think it really matters. His culpability in this is unclear to me, but I do know that he gave a donation to the parish and made jokes about $$ being able to get you what you want. Incidentally, he now receives Communion, though I don't know exactly when he began receiving it again.