“but if they don’t listen to you, then you should embarrass them in public so that they will do teshuvah. “
Do that and you will GUARANTEE them going off the derech. Make sure you are 100% a tzaddik yourself, before you think to give such mussar to someone in a public palce. YOU should NEVER embarrass anyone in public, unless that person is committing a yehareig v’al yaavor.