Sometimes it's something to focus on. Also, you said that what people think of her is very important. So, if she feels she must, as a "good" mother, fight for her kids custody, then that is what she will do.
It is very important for you to detach as much as possible right now, because this is going to hurt. She has lost who she is. She no longer wants to be wife, is unsure about her role as mother, and cannot define herself otherwise. You and the kids, unfortunately, will be bearing the brunt.
You need to take care of yourself and your health, try to sleep etc. Think BD all over again.
