If you follow the scientific exercise method and spend ten minutes a day and stick to it for a long enough time, I think it will get the results you want.
Well, while a lot of scientific research has been done on exercise, there aren't many facts that have been found. Science doesn't equal fact, it just means someone studied something. There are more theories of exercise than there are exercises to do. But here's the thing -- any movement is beneficial, so if you add ten minutes here and ten minutes there and it's ten minutes more than what you were doing before, you will get some benefit above what you're getting now. As to whether it's worth it depends on what you want out of exercise. One problem for you, Mom, is, if I have this right, you have a history of regular exercise that was pretty vigorous, so anything less than that will obviously not give you what you got when you were doing that. That's a problem with those of us who regularly exercised hard for a long period of our lives and then stopped for whatever reason -- our metabolism will be affected differently than someone whose body was never used to exercise. But again, anything in addition to what you're doing now will be of benefit. The only really short exercise program that I've seen touted to give great benefit is interval training, but even that would require at least a half hour. I'm sure the benefits are exaggerated, they always are in this area, but I'm guessing that although you don't exercise as much as you'd like raising your kids keeps you pretty busy, and that's movement and movement is as valuable as exercise if you do enough of it. But if you're asking, if you exercise 10 minutes a day will it help, probably not much, but more than doing nothing.