What is the ruling of Islamic law on a married couple who engaged in marital relations twice during the daytime in Ramadan due to prison circumstances that prevented relations at night, and are they excused in this difficult situation?

You have committed a great sin by breaking your fast, and both you and your wife must repent to Allah and make up the two days. You are required to perform an expiation (kaffarah) of fasting two consecutive months for each day. If you are unable to do so, then you must feed sixty poor people. It is more cautious to perform expiation for each day. As for your wife, she must make up the days, and there is a difference of opinion regarding the necessity of expiation for her.