What is the fate of the home shared by the spouses after divorce, and is the wife entitled to it after she requests the divorce, especially with the presence of a 17-year-old son who testifies to his mother's misconduct towards his father, and the impossibility of one party selling to the other?

The house after divorce belongs to whoever owned it before the divorce. If it was jointly owned by the spouses, then it belongs to them according to their share in it. Registration in official documents under both their names does not change the reality if it does not match the actual situation. So, if the house was owned by the husband and he registered it under his name and his wife's name for her to acquire it after his death, the house remains the property of the husband, because this is considered a will, and he can revoke it before his death.