Is sin and expiation obligatory for one who had intercourse with his wife during the daytime in Ramadan after having intended to fast, knowing that they are travelers?

If Riyadh is your place of residence and you intended to fast, then both of you must make up the missed days. The major expiation (kaffarah (definition) kubra) is incumbent upon the husband, and scholars differ as to whether it is incumbent upon the wife if she consented. However, if your trip to Riyadh was for a purpose and you did not intend to stay for four full days, then you are considered travelers, and there is no expiation upon either of you; only making up the missed days is required. It is obligatory for a Muslim to preserve their fast and to know that the sanctity of Ramadan (definition) is immense.