Is this the kind of relationship that she wants to role model for her daughter? Does she want her daughter to know that women are worthy of men who don't cheat and lie and bully their way through relationships? Then she needs to value herself and her children more than a half-life being bullied by this man.
He sounds controlling and emotionally abusive if he is trying to frighten her off from leaving by threatening her with the loss of her home and children. He is acting as if he has done nothing wrong and her lack of action is only confirming that for him.
That said, I totally understand why she is reacting the way she is. She has spent her married life thinking of them all as a family unit, thinking of their well being together. It must be a shock to realise that her H has been a selfish git and hasn't been considering her and their children for at least as long as this affair. It's an emotional leap to see herself and her children as the ones she has to care for, not him, particuarly if he's been a bully who tells her it is all about him and what he thinks is best for the children.
Obviously, as an outsider there's not much you can do. Three things: be there for her to talk to even if she isn't ready to do anything right away, affirm that she and her children deserve better and make sure that his comments about what she'd be entitled to don't go unchallenged and advise her to get legal advice about the finances/home/residency of children/getting him to leave etc.
I wonder whether if her children were in relationships like this as adults whether she would expect/want them to stay with a partner who treated them like rubbish just for the same reasons, and if not, why is she not worthy of the same respect? Why let her children see that its 'okay' to be treated/treat someone the way she is being treated.
As for the fear of him turning more towards the OW, he isn't some prize to be won, he's an unfaithful, bullying liar. Your friend would be well rid.
It might take her a while to realise that her H and marriage aren't what she thought they were, that she can't make them back to what she thought they were by staying. I guess you just have to be there for her.