First thing of all, you mentioned that your friend is now divorced.
Now the question is have she settled the ancillary matters such as assets and custody? if not get her to file maintenance not only for herself as well as for her children and factoring into the money needed to hire a full time babysitter/helper to look after her children.
In Singapore, women are more or less protected under woman's charter, thus, despite the fact that she might be earning lesser than her husband. So long as there is proof that her children needs her (emotionally) and if she can provide a good environment for her children, I trust that it wont be that difficult for her to gain the custody of the children.
The best thing if your friend is able to get proof of her husband's infidelity (such as get a PI to follow or a photo of steamy text messages exchanged) then the higher the chance the custody of the children will goes to her.
Ask your friend this question, in order to provide a good environment for her children, why isnt she willing to move out of the abusive place?
I believe the above should be able to help in one way or the other. It is not going to be an easy way down the road but once she is done walking past all the obstacles, I am sure she will be able to look back and say to herself that hey it wasnt that difficult and i have managed to face all the obstacles i was given in life. I am now a stronger person.