What is the ruling of Islamic law regarding a man having intercourse with his wife during the daytime in Ramadan after traveling to her, and is he permitted to break his fast because of that?

If you arrive from your journey during the day and have intercourse with your wife, there is no expiation upon you, because you are already excused from fasting due to travel. It is better to abstain from things that break the fast, to avoid the disagreement among scholars. There is no expiation upon the wife either, but she should not have allowed you to have intercourse with her if fasting was obligatory upon her.