Victims of Psychopaths Community Group
Is he or she a sociopath or psychopath? Think we're only talking about serial killers here? Psychopaths, sociopaths and even narcissists come in every walk of life, every career level, and every socio-economic category.

I can move on from him without much feeling, even without animosity. But I never will forget, and I never will foregive. Personally, I think this notion that you have to forgive someone who has treated you so badly and then never will apologize even, is full of it. I think righteous anger, tempered with pity, understaning, and acceptance of who the N/P is, is more beneficial to victims/survivors. It keeps us out of trouble.
I earned my outrage, and I'm not forgiving him! My outrage reminds me I am alive. My outrage is my souvenir. I feel proud of my righteous outrage, and this reduces my shame. So, my self-esteem is higher for recognizing what he is and what he did.
I am coming late into this thread. But you asked, "I dont know if I am allowing him back in just by being cordial and doing what is in the best interest of the kids or I am being sucked in again?"
My feeling (also low contact with my N/P due to co-parenting post-divorce) is that being cordial is a form of being boring, so as not to elicit reactions from him. Why poke the beast? So, it is conciliatory, but not necessarily being sucked in again or endorsing him. It is not foregiving him. It may be understanding what you are dealing with realistically, and choosing not to engage in ongoing battles. Such conciliation is better for the kids as long as they don't see you violating your principles or the principles that "normal" people (nons) should live by.
Compassion might be a strong word when he is affecting me - when he isn't affecting me yeah sure I can have compassion as long as he isnt deliberately playing victim.