In contrast, you can say.."Children who are kept under a tight rein by their parents, often turn out to be rebellious.

Children kept under a tight rein by their parents often rebel. (“turn rebel” doesn’t sound good to me)

The grammatical error is the use of 'turns', rather than 'turn'. The by/under order you have chosen is not incorrect, but it is a little awkward, which is why Chris suggested a more normal order. You can ignore Ruhi's offering, which changed the order correctly, but added more mistakes.

Closest to what you wrote would be. Children who are kept by their parents under a tight rein often turn rebel. (they turn) But, the suggestion sbelow is better, an improvement.

Well!! it would be better if said this way Children who are kept under tight rein by their parents often turn rebels. Don't ask for reasons, ...... because I don't knwo :d