What is the ruling of Islamic law concerning a wife who gestures to strange men, without proof of her having committed adultery, and what is the optimal course of action towards her, given the presence of young and disabled children?

The relationship between spouses should be based on good faith. The husband must control his jealousy so that it is neither a form of dayyouthah (lack of protective jealousy) nor an unwarranted suspicion. If an action by one spouse can be interpreted in two ways, one good and one bad, it should be interpreted in the good light. Nevertheless, the husband should be keen to safeguard his wife's religiosity and protect her from situations of suspicion. If he sees her commit an unlawful act that cannot be reinterpreted, he should admonish her and remind her of Allah. If she repents, then that is good; otherwise, there is no good for him in remaining with her. And Allah protects the children.