I haven't read any of the other posts here, so pardon me if you've already moved beyond this issue.

You describe yourself as being very capable, even owning your own business, being a mother, and also a graduate student. That full plate of yours isn't very conducive to being a graduate student, and since the flexible schedule you were promised never happened, I'd say you've made an excellent case for your departure. Why are you staying at this dysfunctional job that doesn't pay well, has no benefits, and didn't give you the flexible schedule you were promised? You aren't even getting the experience that you were lead to believe that it provided.

You have other income from your own small business, correct? I'm sure that could carry you until the start date for your next job (if you don't quit before getting a new one). There are tons of other job options that you need to look into that at the very least will be better than paying out of pocket your own gas money and mileage for the job your settling for. Honestly, I think you are being used by your boss and probably the admin asst. and you definitely were mislead if not completely lied to about what you would be doing.

Most college students can do quite well with a part-time job after the morning classes.Graduate students can even be teaching assistants, which is right up your alley. Have you looked into those?
Most universities also have a large variety of student job positions that fit very nicely with college courses, which almost always offer flexible scheduling and are usually on-campus or nearby.

I'm sure that you'll have student technology help staff that are employed by your university's computer/technical department (you know, they work in computer labs, answer questions fix printers etc.). Have you considered looking into something like that? It's not a career, it's a job so that you can finish your degree and get on with your chosen career field.

My final recommendation would be to see what you can get in the way of grants and scholarships, as they are sure to help out.