Is expiation required of both spouses, or only one of them, due to sexual intercourse that occurred while they were traveling and fasting in Ramadan, even though they intended to complete the fast despite the hardship?

Both of you, given the circumstances, were travelers, and there is no blame upon you for breaking the fast, nor is there any sin upon you, whether you broke the fast by intercourse or otherwise. Expiation (kaffarah) is not obligatory upon either of you; rather, each of you must only make up for that day.

A traveler is permitted to break the fast. And if one intended to fast and then engaged in intercourse, there is no expiation (kaffarah) upon them, because fasting is not obligatory upon them during travel.