Thank you for your helpful reply to my question. There are some constructive points there, but I fear the situation is even harder than I might have painted. There doesn't seem to be any physical violence, and we find from the ABI.pdf document that you suggested, that the abuse is mainly emotional and Jim certainly scores very highly on that. However, it makes him especially harder to catch out or expose, because he manipulates and reframes everything so that he looks good.
I think our daughter knows that he won't change from the inside, but from the outside he is pressing all the correct buttons for her, so that at the moment she believes it is less harmful to stay with him than to leave him - as well as being less expensive. He is the "house father", whilst she is still working on a good salary. She doesn't at present see the damage he is doing to the children, the abuse of whom is again in the ‘emotional' category.
It is even more difficult for us to help, because she is very much against counselling therapy and psychology in general and becomes aggressive to her mum and me if we make suggestions or suggest web pages or books. She is "too busy for that sort of thing".
Whereas I agree with and understand everything you have pointed out, whilst appreciating your reply immensely, it appears to me that there is little we can do except put up with his controlling behaviour, and make sure, as you say that she knows we are there for her all the time.
Any comments would be gratefully received, although I know this is a tricky one. Most of professionals I meet socially or on web pages say that the profession can do nothing for psychopaths and the only advice is to "RUN". If psychiatrists say this, what chance have we got to help either our daughter or ourselves live with this destructive but charming and empty person, let alone expose him to my daughter for what he really is?