How can my partner stop his ex from poisoning his teenage daughters?

General

I am struggling here to know how to support my partner in his quest to maintain a healthy relationship with his daughters. They are both victims of a tirade of emotional blackmail by their mother who does everything she can to poison them against him and me, his partner. Now that he has pretty much reduced his contact with their mother she leans on them for suppport, tells them that she is going to die, and cries continually. Their response is obviously to care for her and are becoming increasingly hostile to my partner, who has done everything he can for them, bar remain with their mother after finding out of her affairs. Despite everything, he has refused to make negative comments about her and kept his anger to himself, in order to protect them from knowing the worst.
He loves his daughters and is a devoted father, and hates the idea that they possibly now hate him and cannot understand anything from his point of view. His ex still remains in the family home, has a fantastic maintenance deal while he rents a flat, lives very frugally and is unable to afford to buy anything for the foreseeable future. Much of the maintenance settlement was forged out of his guilt of having to leave his daughters. However, his ex rarely spends money on the girls, pleading poverty all the time. She is my worst nightmare as a potential ex. She is also a class manipulator. Where on earth does my partner go from here and how can I help the situation?