Hi. You did not enter the text to which this question refers, which makes it impossible for it to be answered. However, I will try to help you as best I can.
The expression "give a long rope" refers to the possibility of giving freedom to someone, so that that person can accomplish something. Accordingly, the phrase "Children must give a long rope to their parents" may represent the children's need to allow their parents to have a certain freedom within their lives, such as freedom to feel insecure, to be able to advise, among others situations. In this case, to answer your question, you should look in your text for a time when someone's parents needed to do something about their children, but they didn't feel comfortable doing that, because they didn't feel they had the freedom to do so.
