Chances are child care assistance could help with the cost of your child care but even if you worked part time during the day you would have an income.
I have found when I worked outside the home that I was able to get much more done at home. There is time to do all this plus more like homework and spending time with the family. Ask any working mother at this site.
You can work in the school system, as a substitute, or maybe as a teacher assistant, working with kids with special needs as an aid is very rewarding too.
There are probably several Mothers-Day-Out programs in your area too, they might be needing teachers too. They are usually during school hours and only a few days per week and your little one could go along. I did find that I hated child care when I had kids at home and choose to do something else until they were older. I was a bridal consultant, a wedding planner, a computer technical support person in a call center, worked for over 10 years with persons who have developmental disabilities, and some other part time jobs. What I am saying is there are all kinds of jobs out there and most are rewarding in any kind of sense even outside of the paycheck.
You could check with your employment office and see if there are individuals needing a helper of some sort too.
I have ALWAYS found that when I worked outside of the home I felt better about everything. I had a break from being at home all the time, I had the ability to have extra spending money so I didn't feel so dependent on my husband.
Another thought too, if you only have one child home all day why are you stressed out about the house? If you schedule your time well I don't understand why the washer and dryer aren't running while you are doing something else. I choose to not stress about the house and the kids have chores. Their rooms are their responsibility and papa helps them. If their rooms are not at an acceptable level they don't get certain privileges. They have a job to do just like everyone else. It's their responsibility to do their jobs.
A family meeting sounds like a good idea at this point. Each person should have assigned jobs. Even hubby. My hubby helps the kids clean their rooms, does the dishes and takes out the trash. He is also responsible for the outside work. If he chooses not to do it he is welcome to hire someone to do it for him. Not my problem, I just want them done, he can pay them.
There is no reason school age kids are not doing dishes after dinner and putting their laundry in hampers and learning to wash it themselves, with supervision of course until they are proficient. They should have chores, they live there too.