Is it right to improve the husband's image in front of his wife, who suffers from his bad behavior, and to remind her of his good deeds, for fear of the children's emotional well-being due to divorce?

Your effort to reconcile the spouses and remind the wife of her husband's good qualities is commendable and religiously مطلوب (desirable). If the wife becomes aware of her husband's sinful relationship with other women, she should advise him and remind him of the seriousness of his action and its dire consequences. She should also threaten to inform the families of these women or the responsible authorities so that he may be deterred. She should be patient with him to avoid the negative consequences of divorce on the children. However, it is not permissible to accuse him of zina (fornication/adultery) without clear proof, lest she fall into the prohibited act of qadhf (false accusation).