Is a single repudiation incurred by the utterance "You are divorced, divorced, divorced" with the intention of divorce and separation, and is it permissible for the husband to take his wife back after the intervention of friends and her pledge to improve her behavior, especially since they have four children?

If by uttering "divorced, divorced, divorced" you only intended to emphasize a single divorce, then only one divorce has occurred for your wife. However, if you intended to effect three divorces, or if this divorce completed the three divorces, then your wife has become irrevocably divorced from you (baynunah kubra). She is not permissible for you until she marries another husband, he consummates the marriage with her, and then he divorces her or dies, and her waiting period (iddah) expires.