All perfect praise be to Allah, The Lord of the Worlds. I testify that none is worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
What we understand from your question is that your husband is required to offer expiation due to having sexual intercourse with you during the daytime in Ramadan and does not want to pay it because he believes that it is not obligatory upon him because he did this while he was ignorant of the ruling. He is really mistaken. The correct opinion is that the expiation is obligatory upon him, even if he did what he did while being ignorant of its ruling. Expiation of having sexual intercourse during the daytime in Ramadan cannot clear one's liability unless it is observed according to the prescribed order of the three courses of action. Accordingly, it is not valid for you to pay it on his behalf since he is able to fast. Also, it is not valid to pay it except with his permission because expiation is an act of worship and amongst the ruling of its validity is to have the intention to do it. So, what you have to do now is to try, by all possible means, to convince him—kindly, leniently and wisely—that expiation is obligatory upon him. We ask Allah to help and guide us and you.
Allah Knows best.