While it's preferable to own your own business, most women - and men for that matter, simply do not have the wherewithal, and if the now ex-wife and mother made no prior preparations, she and her children will certainly find themselves in a world of hurt.
I assume that her sudden need would probably not afford her the luxury of spending anything - including time for schooling to learn a career. Assuming she has no skilled trade experience at all, she would probably be forced to find almost any income pretty quick.
She should seek a job with 'on the job' training at a job she could actually make a living at, then after a few months or perhaps a bit longer, she could look into becoming an independent contractor and do that work from home full time, or after learning the new skill, quit the job that trained her and use that experience at a new job for more money and maybe better hours, conditions etc.
At any rate, her goal would be to learn a job that eventually she might be able to do from home, either salaried or contracted. There wouldn't be worries about finances other than to stash away 40% or so for taxes and savings.