I have done teaching for summer school(8am-12pm) and mystery shopping. In my particular situation, I made more money summer school teaching than mystery shopping. You won't be able to do any high pay shops with a child. You will have many more options if someone can look after the child while you do shops. But, then again, the whole reason you are not doing summer school is to spend more time around your child, right?
I'm not knocking mystery shopping, but you will spend just as many hours doing MS as teaching summer school for less money. MS isn't difficult, but it does take some time to find your groove. When I first started MS work, teaching was easier because I had had a lot more practice at it. MS was more stressful for me than teaching algebra, especially when it was a shop like Mcdonald's with all their "requirements" you had to remember.......all for less pay than teaching summer school :/
But, if money isn't really a factor, MS is great. I love going out to get some meals for free. My grocery expenditure for the last three weeks was $30 because I'm eating enough in my shops to not have to shop for food or do any cooking or cleaning of dishes. But, I am also single with no kids.