What is the ruling on conjugal relations between spouses if it later becomes apparent that the wife has not exited her state of ihram from Umrah?

Your wife must shorten her hair to exit the state of ihram from 'Umrah. There is no penalty upon her for the intercourse that occurred because she did so believing that she had already exited the state of ihram from 'Umrah. Some scholars are of the opinion that intercourse after Sa'y and before shaving or shortening the hair necessitates a fidyah (expiation), even if it was due to forgetfulness or ignorance. This fidyah is optional (fasting three days, or feeding six needy persons, or sacrificing a sheep).