Since when is it her job to manage her partner?!
He knows he's being abusive. He can hear the screaming coming out of his own mouth. He knows he's doing it to his partner and in front of his children, which is abusive to them too.
He can decide for himself that his own behaviour is unacceptable and that he needs to do something about it, like see a doctor, if it's not his true personality and he thinks there's something wrong. It's not for OP to have to help him find the cause, at her own instigation. It's ok to want to date someone who takes responsibility for themselves and their own behaviour and their own health. It's ok to not want to feel she has to mother a grown adult who she didn't give birth to.
Instead he's actually just another abusive man. OP says his opinion is he doesn't need to change. He's had therapy and this is still his opinion. He's fine with abusing his partner and children. There's nothing to work with.
OP your children don't need this abuser in their lives. It's not good for them, it's actively harmful for them to witness domestic abuse, whic is what this is.
Be glad he's fucked off and hope he doesn't return. Don't make a fuss about childcare or them missing him etc and let him fade out of their lives. You don't need him using them to control you for the next 16 years and they don't need to spend their childhood treading on eggshells around a volatile man who consistently puts his own wants above their basic needs.
They're small with no real way of understanding it or expressing it, especially as they've known no different, but there's no way the children were feeling safe and secure whilst you were together. Ex is not going to morph into a different person just because you've split up. He'll always put himself first. He'll probably go on to abuse subsequent partners too, so that's more domestic abuse his children will witness. As the children grow up and start getting a mind of their own they'll come in for direct abuse from him themselves. It's no way for the children to live.
They're young and they'll get over his absence far easier than they'll get over a lifetime of trauma from staying in touch.