I'm not sure what's fair in this situation....

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I have been watching a 2 year old for over a year now. His mom and I get along just fine, and I've very rarely had to tell her I couldn't make it. When I first started working for her I made $10 and worked around 15 hours every two weeks. In January she knocked me down to $7 an hour (she wanted to only pay me $6 an hour, she said because it was "fair") and even though I'm working every week now, I usually only get 1 or 2 days and usually no more than 3 or 4 hours. This week I only made $18. She is now looking into getting a new full time job and needs me for 50 hours a week, not only to watch the 2 year old, but to use my car to pick up his 11 year old sister from school every day. I told her I'd work for $6, well under minimum wage. I figured she'd talk me down a little and I get that, but she is now telling me the most she'll pay me is $125 a week, to watch both kids and pick her daughter up from school. She said it was what people are usually charging. First of all, who works 50 hours a week for only $100? Also, do they factor in having to go pick up a child from school, having to use their own car? I told her I'd work it for now, but she should consider children's cabinet for the 2 year old and just having me pick up the 11 year old. She and I haven't decided anything yet, because she is not sure about even taking this new job. I can't work for 50 hours a week and being paid that low. Did I do the right thing? Am I expecting too much? Advice?