I think a family court would consider it reasonable to stipulate that a new girlfriend should be introduced gradually to the children, and should not stay overnight until some time has elapsed.
Unless your daughter wanted to involve her children as witness to his aggressive behaviour, which I'm guessing she wouldn't, it is just her word against his.
Might it be best for your daughter to conduct any discussions regarding sensible routines and arrangements for the children, plus any other concerns she may have, by way of e-mail? (Perhaps she could say that, in the light of his recent aggressive behaviour in front of the children, she did not wish to discuss these matters face-to-face.)
If her ex doesn't respond, she will have evidence of his unwillingness to discuss the matter sensibly. She will also have evidence that he doesn't deny his aggressive behaviour. If he does reply,using abusive or threatening language, this will support her concerns regarding overnight access. She would not, of course, have to be drawn into slanging matches with him, although the occasional angry remark might lead him to be less cautious about his own responses. Sometimes people are less careful about what they say in e-mails.
If he telephones and makes further aggressive remarks, does anyone know if it is legal for the call to be recorded?
What do the children feel about all this - were they upset when they didn't see him for six weeks?