from my research:
1: women pray at home is better at a certain situation
It was during the times of Sahabas that women were stopped from going to the masjid since the environment became risky. As wealth flowed, women starting making extravagant displays in the masjids, stealing the attention of the worshippers. But in the absence of any hadith i cannot conclude that the prayer at home will be better than prayer being performed in masjid in Mecca or Madina..
There is only one Hadith, which perhaps could have been misunderstood to mean that women should not go to the mosque. That Hadith is as follows:
Abdullah Bin Mas’ud reported the Prophet (pbuh) as saying: It is more excellent for a woman to pray in her house than in her courtyard, and more excellent for her to pray in her private chamber than in her house. [Sunan Abu Dawood Vol.1 Chapter 204 Hadith No.570]
If you base your conclusion only on this single Hadith, then you may wrongly conclude that it is not advisable or preferable for women to go to the mosque. However, your conclusion cannot be based only on one Hadith neglecting or ignoring all the other Ahadith. The context of the Hadith is also very important.
The Prophet (pbuh) said that if a person prays in the mosque he gets 27 times more blessings (Sawab). Some women argued that they had infants at home and other household work and therefore could not go to the mosque. Thus, the men would have a greater advantage than women for receiving such blessings. It is then that the Prophet (pbuh) said the above Hadith.
Hence, the conclusion is that in situations where women have infants and household work, which too is an important duty that cannot be neglected, women would not be deprived of the sawaab (blessings) if they pray in their own homes.