Praise be to Allah.
We put this question to Shaykh Muhammad ibn Saalih al-‘Uthaymeen, may Allaah preserve him, who answered as follows:
If they both agree, then that is fine. But if the wife whose day it is insists on it, then it is still her day. But I advise women to take things easy with regard to this matter, because whoever makes things easy (for others), Allaah will make things easy for him. The day of Eid should be a day of coming together so that all the people may share the joy of their Eid. And Allaah knows best.