I work at home. I have one child, who is now 12 years old. She is old enough to (somewhat) take care of herself during the summer, but I still have to make sure that I dedicate enough free time to go and do things with her because, let's face it, 12 years old is still young enough that she gets bored quite easily.
Therefore, I have it factored in that I work very, very hard during the school year and I tailor off during the summer months, when she's home on school break (and my authors also reduce their workloads, as they have their own children home during the summer). However, I freelance for a reason; I can do this. If you're actually working a 40+hr/week job for a company at home, you won't be allowed this luxury.
I've been working at home since my daughter started Kindergarten. I started my own freelance editorial business. I was lucky; I've belonged to a professional writing organization since 1993 and my English scores have always been As or better. I understand fiction writing, can critique it, and have excellent English grammar skills. I was lucky and landed an acquiring editor job with an e-publisher. I also proofread for a small independent publisher. I also get a few other small jobs, but really, I have to watch how much work I take on so I can balance it with childcare as well as household work/errands/etc.
Last year, I made the most money ever: $8500. That's not a lot, is it? Could I make more? Heavens, yes! If my child was old enough so that she doesn't constantly need me, I could solicit more editorial side jobs. However, she has a Sensory issue/is special needs and so is quite needy.
I work, so that I have work experience and so that we have some extra income coming in. We do not live off my income; it supplements our lifestyle. You never know when you might have to reenter the job market, and this way, I can show/prove that I have been working since I've been home with my daughter, which has now been 7 years. Not saying being an at-home mother isn't a job and isn't a full-time job--it is, because I do it--but having actual work experience/having worked for other companies while I've been at home will hopefully give me a leg-up if I ever need to look for a job outside the home.
If you need to make lots of money, then you're going to seriously have to think about what it is you can do from home that will allow you to make that much money and still be able to take care of your children. Those jobs are, alas, very seldom. I see having four children at those ages to be a major handicap in finding something that pays well, unless you're going to be able to put them into daycare--and that's probably not why you want to work at home, as you'd prefer to be home with them. I also see serious money meaning 40 hrs/week, if not more. You should know that I in no way, shape, or form, am at all adequately compensated for the time I spend editing, and I definitely get NO pay for all of my office/administration time. That, I eat. I do not expect to make megabucks, working at home, nor have I ever thought that I would.
At the end of 2012, I will have edited and released/published 18 e-books--not to mention I'll probably have proofed about 6 other books, and I also work for a college professor, who is currently writing his dissertation in book form. And even with all that work, the pay doesn't match up with the time expended. But the ability to remain home/be here for my daughter--THAT is why I do this. When she's graduated from high school, then I can aggressively pursue more jobs and work 40+ hr weeks. Right now, that isn't feasible.