Don't you think if those kinds of jobs were all grouped together some where we'd all be working from home?
If you work at home you have to put your kids in child care and commit to an employer. If you have any business calls they won't give you the time of day if there's a crying baby, a barking dog, and meowing cat, etc...they want to talk to a professional in an office not a mom who is paying half attention to her work while having kids running underfoot.
The only businesses that do this are ones that have long faithful employees who ask if they can work from home. They take their kids to child care before going on the clock then they work all day.
If you want to do stuff on the computer then put some ads in the local college papers that you'll do term papers, research essays, resume's, etc...it will be sporadic but some extra income.
I work 3 part time jobs. I take in ironing. I wait until the kids are in bed and iron up to 3 or 4 hours if I have that many garments.
I clean houses, most often my father in laws house, he pays me with a gasoline card. I get to fill up my van up to several hundred dollars each month. He's never told me to cut my costs but did tell me if there is ever a pop or food item on the charge he'll cancel the card that day. No reprieve.
I work in the clothing store owned by a gymnastics/dance studio. I make performance costumes, sell items, do paperwork, stuff envelopes, hand address envelopes, clean the facility if needed, take out the trash when it's full, clean the entire building's carpets once a year or so, I work my hiney off and do not get a single penny. I get the kids dance and gym classes for free. I don't get paid I get a scholarship for them.
So if you want to sit at home and do work while your kids are there you're misinformed that this type of job really exists. If it did every single stay at home mom would be doing them already.
They don't exist unless you have already worked for a company and proven you can work at home and accomplish your tasks and will be alone during the day to do your job. They know you and how your work is well before this conversation takes place.
No one is going to pay you to stay home and have your kids at home, they aren't going to. You will have to take your kids to child care and work, just like a real job.
If you want to work for yourself then figure out what jobs you'll do and post them on your FB page, put up fliers in the laundry mats, Walmart job boards, and any college dorm you can get to. That may be a good niche for you. Doing stuff on the computer takes time and doing research papers and stuff like that is a needed thing.