Asalaamualaikum wa rehmatullahi wa barakaatuhu mufti sahab. Could you please quote the hadith shareef in sahih Bukhaari in full (along with the hadith number) in which Hazrat Aeisha(radhiallahu anha) tells us that if Nabi(salallahu alaihi wasallam) knew about the conduct and situation of women in her times, He(salallahu alaihi wasallam) would have definitely prevented women from going to the masaajid (as on Eid prayers)
Answer:
In the name of Allah, the most Beneficent, the most Merciful.
Sayyidna Abdullah Ibn Umar 
narrates that the Prophet of Allah 
has said: “When your women seek permission from you to go to the Masjid then do not stop them” (Sahih Bukhari p 120 v 1)
Initially, in the time of the Prophet of Allah women were allowed to attend the Masjid for prayers.
However, during the time of Sayyidna Umar , when Fitnahs (trials and temptation) started to creep into Islam, women were told not to offer their prayers in the Masjid. At that moment, the women were not pleased with Sayyidna Umar decision, so they decided to go to Sayyidah Aisha 
to see what she made of it. When they went to her she then narrated the following Hadeeth. (Fatawa Darul Uloom Deoband p 47 v 3)
Umrah Bint Abdur Rahman narrates that Sayyidah Aisha said : “ If the Prophet of Allah was to know the situation of today’s women, then he would surely stop them from coming to the Masjids, just like the women of Bani Israeel were stopped (from entering their places of Worship). The narrator says: “I said to Umrah were they stopped?”, she replied: “yes”. (Sahih Bukhari p.120 v.1, Hadeeth number 869)
We also come to know from several other Ahadeeth that a woman praying in her home is much better than her praying in the Masjid.
It is narrated from Umm Humayd , the wife of Abu Humayd al-Saa’idi, that she came to the Prophet of Allah and said: “O Prophet of Allah, I love to pray with you.” He said: “I know that you love to pray with me, but your praying in your room is better for you than your praying in your house, and your praying in your house is better for you than your praying in your courtyard, and your praying in your courtyard is better for you than your praying in the mosque of your people, and your praying in the mosque of your people is better for you than your praying in my mosque.” So she gave orders that a ‘mosque’ be built for her in the innermost and darkest part of her house, and she used to pray there until she met Allah (i.e., died). (Musnad Ahmad)
Sayyidna Abdullah Ibn Masood narrates that the Prophet of Allah said: “A woman’s prayer in her house is much more merit worthy for her than her praying in her courtyard, and a woman’s prayer in that discreet portion of the house is much more merit worthy for her than her praying in that portion of the house where it is open” (Sunan Abu Dawud p 94 v 1)
Sayyidna Abdullah Ibn Umar narrates that the Prophet of Allah has said: “Do not stop your women from coming to the Masjid, however, there houses are better for them” (Sunan Abu Dawud p 94 v 1)
From these Ahadeeth, we realise the virtue that women receive for offering their prayers in their homes.
In the modern era where women are roaming around the markets, shopping centre, roads, streets it seems rather unfair to shun them from the mosques. The view of my respected teachers are that women will be allowed to pray at the mosque provided there are separate entrances and facilities for them to pray and that they are far away from mixing with or being viewed by strange men.
Only Allah Knows Best
Written by Molana Ishaaq Hussain
Checked and approved by Mufti Mohammed Tosir Miah
Darul Ifta Birmingham.