Is it permissible for a young man to leave his divorced fiancée who has a child from a previous marriage, due to his psychological distress from her communication with her child, and his belief that this will open a door to problems he does not want in his new marital life?

If your parents object to your marriage to a specific woman, the default rule is that you must obey them, unless there is an overriding benefit [in marrying her]. It is the husband's right to refuse the residence of his wife's son from another man in his home, but he does not have the right to prevent her from seeing her son or from her son visiting her in a reasonable manner. The Maliki jurists stipulated that young children should visit their mother every day, and older children once a week. It is not permissible for the wife to sever ties with her son, nor is it permissible for the husband to demand that of her, because that would be an incitement to severing kinship ties, which is forbidden. If you fear that this matter will be a cause of future disputes, then it is better to seek someone else.