Firstly: 

It is prescribed for Muslim women to go out to the prayer place on the day of Eid, to offer the Eid prayer with the Muslims, not wearing perfume and not showing off any adornment. 

Al-Bukhaari (324) and Muslim (890) narrated that Umm ‘Atiyyah (may Allah be pleased with her) said: The Messenger of Allah (blessings and peace of Allah be upon him) commanded us to bring out on al-Fitr and al-Adha the girls who had reached puberty, menstruating women and women in seclusion. The menstruating women were to keep away from the prayer but to witness goodness and the du’aa’ of the Muslims. I said: O Messenger of Allah, one of us may not have a jilbaab. He said: “Let her sister lend her a jilbaab to wear.” 

The Standing Committee was asked: 

Is Eid prayer obligatory for women, and if it is obligatory, should she pray it at home or in the prayer place? 

They replied: 

It is not obligatory for women, rather it is Sunnah for them, and they should offer this prayer in the prayer place with the Muslims, because the Prophet (lettings and peace of Allah be upon him) instructed them to do that.

End quote from Fataawa al-Lajnah ad-Daa’imah (8/284) 

See also the answer to question no. 49011

Secondly: 

It is not prescribed for women to offer the Eid prayer in their houses, led by one of their number, if they are able to go out to the prayer place to offer the prayer with the Muslims. It is also not prescribed for them to set aside a separate place for the women where they offer the prayer on their own, because that comes under the heading of innovation (bid‘ah) 

Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: 

Is it permissible for a woman to offer the Eid prayer in her house? 

He replied: what is prescribed for women is to offer the Eid prayer in the Eid prayer place with the men, because of the hadeeth of Umm ‘Atiyyah (may Allah be pleased with her). Therefore the Sunnah is for the women to go out to the Eid prayer place with the men. As for women offering the Eid prayer in their houses, I know of no Sunnah concerning that.

End quote from Fataawa Noor ‘ala ad-Darb (189/8) 

He was also asked: 

A woman is asking about Eid prayer for women, because we do not have any prayer place for women, so the women gather in my house and I lead them in offering the Eid prayer. What is the ruling concerning that? Please note that my house is private and far away from the men. 

He replied: 

The ruling concerning that is that this comes under the heading of innovation. Eid prayer can only be offered in congregation with the men. Women are instructed to go out to the Eid prayer place and offer the prayer with the men; they should be behind them and avoid mixing with them. 

With regard to doing the Eid prayer in her house, this is a grave mistake. There is no report from the Prophet (blessings and peace of Allah be upon him and his family) or from his Companions that the women offered the Eid prayer in their houses.

End quote from Fataawa Noor ‘ala ad-Darb (189/9) 

And Allah knows best.