Sounds like she needs a break. Any possibility someone in her or the father's family could take them or even one of them for a month? My brothers and I lived with an aunt and her family when my mother was about to break down.
I would start with my family physician to get a prescription for an antidepressant/antianxiety medication.
She also needs to start counseling for herself. It should be included in her insurance. As a teacher she may earn too much to get her kids on state or federal insurance unless the father has been court ordered to provide insurance. They may qualify because of that. It's worth asking. Call the state office of human resources.
She needs to also get help with managing her income. Dave Ramsey's books and other presentations are often recommended. You could research that for her. I suggest she start by writing down a budget. She can get help doing this using info and forms from the Internet.
I suggest that you might be able to help her by helping her to write a list of problems and next to each one brainstorm and write down possible solutions. I'd use on page/problem/situation. Then put those in order of priority. Then make a plan.