What is the ruling of Sharia on a wife who is proven to have gone out with a foreign man and committed adultery, and sent him pictures, while she vehemently denies it after being confronted with the evidence, and what is the optimal course of action for the husband in this situation, given that they have a daughter?

The presence of suspicious calls on the wife's phone is strong evidence of an illicit relationship, and jealousy in this case is commendable. You should be patient with her and inform her of your desire for her righteousness, while being firm in obliging her to observe modesty and hijab, and preventing her from mixing with non-mahram men or going out without your permission. Be keen to teach her matters of her religion, and to purify her soul with faith, and accompany her to gatherings of goodness. Be a good role model for her. If she becomes righteous, then that is excellent. But if doubt persists, then divorcing her is better, especially if she neglects her obligatory duties towards Allah. "Three people supplicate to Allah, but their supplication is not answered: a man who had a bad-tempered wife and did not divorce her."