I work at home as an editor for an e-publishing company as well as doing some freelance work on the side. I own my own editing business. I make about $4,000-$5,000/YEAR and this year, I might make $7,000. Really. And that's working anywhere from 20 hours/wk up to and over 40 hours/wk. I try to maintain part-time hours, because my daughter/family are a top priority, but sometimes deadlines make working a priority. I have looked and have not found jobs where the money just pours in for little work or effort or for just a few hours of work. I think those are a fairy tale!
I definitely am not doing a job at home that is supporting my family!
However, what it does do is allow me to have a little money for "extra" things (like paying for my daughter's dance lessons, which we couldn't afford if I didn't make a little pin money) and to keep an updated resume of work that shows I am "working" while I'm home raising my daughter (Starting in Nov I will have worked for the e-publisher for six years, so I have a good, long-term work relationship with them, and another small publisher I have a three-year working relationship.). It allows me to pursue my passion--writing, editing, the publishing industry--while giving our family breathing space and stress reduction (having two working full-time parents out of the house; did that for five years. Wasn't working with our special needs daughter. My staying home is the best thing we've ever done. But my husband makes over $80,000/yr, has good medical and dental, has 401k and other great perks from his company, so I can afford to work at home/not make a ton of money.).
Could I make a lot of money? Sure. If I don't want to be a mother to my daughter or a wife to my husband. But I (and my husband) have decided that it's not important how much money I bring in as long as I bring something in. What's more important is that I am available whenever my daughter needs me (school activities, school vacation days, getting the household errands done so that we have the weekends open to do family stuff [That was the hardest when I worked full time outside the home; the weekends were always packed full of errands so that we could never enjoy family time or enjoy the weekends], or being available to nurse a sick daughter). Working at home allowed me to be a caregiver to my husband for the past two months while he recovered from a tibia-plateau reduction surgery (broke leg on Aug 22, 2011; just went back to work Oct 31, 2011). We couldn't have managed that if I didn't work at home.
I think the $2000/month you're thinking is quite unrealistic. And it takes time to get anything started, especially if you're starting a business from scratch. Remember that anything you have to use to start/run your business will be deducted from what you make--most people who start their own business are often in "the red" and don't make any money for a good five years. If you can stick it out for five years and actually make some money, you're doing good.
If you are able to get a job with a company where you can telecommute, you might have a better chance at making some money. However, it isn't easy working at home with small children. In fact, I worked out of the house until my daughter entered Kindergarten; then I stayed home and started my own business. Her being in school helps big time, because I get those dedicated hours to work on my business and/or run errands and get other household chores done.
There are a lot of things to juggle and consider when working from home. The least is childcare and how/when the household chores are going to get done.