I acknowledge what you are saying about seeing improved behaviors in some ways.

However, I stand by my original stance: the DBT workbook did not prevent him from accusing you of abuse, raising his voice at you in front of the child, and yelling that he will call the police and social services.

I also think that instead of addressing his abuse directly with him, that you are learning how to adjust and modify YOUR behaviors to accommodate his insatiable needs around rejection, perceived attacks, and whatnot. This is basically modifying how you respond so that you don't trigger him into abusive behavior. Again, I think you're coddling him rather than addressing the fact that he is abusive.