Welcome to the forum!
Your question is very difficult to answer because shops and shopping vary so much around the country. As a general rule of thumb, it is very difficult to make a living doing shops. The pay is generally fairly low, the pay tends to be fairly slow and to do enough shops to make a living at it you also will need money to front for required purchases that will be reimbursed. While you could spend time at home with your son searching for work, I suspect that the drop in care would eat much of your profitability very quickly.
These days there is a lot of shopper competition for a reduced number of clients being shopped. IF you happen to be in an area where there is not a lot of shopper competition, and IF there are a lot of companies shopping your area, and IF you are able to set up routes of shops then it might make sense to put your son in care for a few hours while you perform them, pick him up and head home to do reports.
There are folks on this forum who DO make a living doing shops. They tend to spend a lot of time on the road and do a lot of shops out of their normal community. I am on the edge of a small city with 6 communities beyond that in my 'shopping area'. I do those jobs that I see that make financial sense and in an average month that is $1000-$1200 with about half of that being reimbursements for money I have spent for things I found useful. It works for me because I am retired so have the freedom and flexibility to work when I please and limited goals of what will actually be paid for out of shopping proceeds. Luckily my living expenses are low, so the $500-600 of actual fees earned goes a long way to cover my living expenses that were not financed by reimbursements. (I've never seen a shop that would reimburse me for my mortgage or utility bills or health insurance, etc.)