Are we commanded to pray Eid prayer at the Mosque as opposed to the other prayer at home?
No, Salat Al Eid is a Shaaira i.e. It is a worship which has to be openly shown. The Prophet, peace be upon him, urged women to go to the Eid Musalla (place of prayer), even those who have their menses should go and sit aside from praying area but they need to attend the Shaaira.The Eid Musalla, according to the Sunnah, should be out of the residential area on the borders of a town and all Muslims should go to this Musalla. Unfortunately, this Sunnah is not followed.