Considering how she willfully neglects the children, you should concentrate on their safety, first. You can't force her to be a good parent, but you can take steps to protect your kids from her.
I think you need to consult legal advice, to see your available options and rights. Find out where you can turn (child services, police, .....something). I've heard that most lawyers will give an initial consultation, free of charge.
You need to see what to do if you have to take the children and leave. I mean, you can't trust her to take care of the baby while you're trying to work.
She thinks she holds all the cards just b/c she's the mother. Apparently, you think so as well. It's not always the case these days.
She is a mean bully!
It is not about what you feel should work in your M. It is about doing the work that gets the right results. Do what works!