WHAT IF . . . . . . .
I've lived this situation. I know what it is like to work at a job you dislike but your income is valuable to the family. I did quit my job only after I had lined up children to babysit in my home to supplement the income. I knew that being home and babysitting other children would not give me flexibility in my day, but it didn't matter to me. I didn't have grade school children at the time as in this case scenario. I had one child and he was one at the time. In the end, it worked for me as I was home with my child and I babysat two other children near his age and they became great friends. I earned the extra needed income for our family.
Perhaps in this scenario the wife could stay home and reduce her expenses by $400 through scratch cooking, cancelling some services such as cablevision and learning to live a frugal life. But in my experience some people are not meant for the frugal life and after a period of time they can fall off the wagon and revert to old spending habits. However in saying that, this wife could go ahead and see if they could possibly live on less money while she is working and stockpile money into savings. She could set a deadline for 1 year and see if by then it would be possible to quit her job because she was reducing expenses, paying off debt and getting money into savings. Just knowing that you have a deadline for possibly quitting your job brings about a change in attitude.
In this economy I would be hard pressed to quit a job and stay home if there was not going to be enough money to pay my bills. Instead I would do whatever it took to find a way to put a positive spin on my job even if it was only that I was earning a paycheck.