his behaviour -abhorrent as it is - is also really scary. he seems so detached from reality. He's also refusing to even acknowledge anybody elses reality and acts like he has absolutely no empathy or feelings of responsibility towards his family.
i would be asking for psychiatric assessment on him before i allowed him to have unsupervised-by-myself access to the dc. the invoicing, the begrudgingly giving of crumbs, the deliberate mental torture and forcing you to beg - it's the behaviour of psycho/sociopaths.
he has no relationship with his kids, he has no connection with them. he sees them as possessions - his possessions - to be used and controlled according to his will and agenda. what happens if he has the dc on his own and he has another psychotic episode where he feels they are draining his resources - money, time, energy and having a detrimental effect on his 'reputation'? he could easily physically harm them and believe he was right for doing so.
i'd give him what he wants - police and ss involvement. let him watch you all slap him with a restraining/non-mol order. let him see his behaviour written down on record for the 'world' to see. At some point he has to snap out of the reality in his head and engage with the one you all belong to. that could be a tipping point for him and you need to ensure that you and the dc are kept well away and safe from him.