I'm really sorry you are going through this, you clearly love him a lot and are hurting so much
But from someone not emotionally involved in this, it seems clear he has been planning this for a while, starting with the decision to work away when he didn't need to. It sounds like you have bent over backwards to please him. I know it's really hard, but stop calling him , and certainly stop begging him to take you back. While break ups are rarely 100%/0% blame, his behaviour towards you has been appalling and it's him that should be begging for your forgiveness. Don't give him that power.
Who cares for the child he has 50/50 custody of when he's gone all week? You I'm assuming? To say he doesn't care if you both don't see each other's kids is really horrible. I don't want to preempt or upset you, but be prepared there maybe some admitting or evidence of cheating. The comment he has become close friends with the girls, coupled with his past of cheating come across as him edging towards revealing someone has happened.