What is the ruling of the Shari'ah on dealing with a wife who loves another man, continues to communicate with him, and refuses to obey her family, knowing that she is asking for a divorce and has a son? And are she and her son entitled to financial support?

If a mother orders her son to divorce his wife, he is not obliged to obey her. The evidence for this is in the Hadith of Ibn Umar concerning the father.

As for the maintenance of your child, it is obligatory upon you as long as he is in need. And the maintenance of your wife is binding upon you as long as she is under your marital bond, unless she is disobedient (nashizah) by leaving the house despite your forbidding her from doing so.

You are obligated to exercise guardianship over your wife by preventing her from evil deeds and closing the doors to temptations. If she repents and becomes upright, it is better to retain her. But if suspicion arises from her, then it is not appropriate to retain her.