It is better for a woman to pray in her house than in the mosque, whether that is an obligatory or supererogatory (naafil) prayer, including Taraweeh prayer.
The scholars of the Standing Committee said:
A woman’s praying in her house is better for her than her praying in the mosque, whether it is an obligatory or supererogatory prayer, Taraweeh or otherwise.
A woman may pray Taraweeh at home according to whatever she is able to do, paying attention to the Sunnah as much as possible. If she has memorised the entire Book of Allah and she is able to make the prayer lengthy, then she may pray eleven rak‘ahs, or thirteen, praying two by two, then praying Witr at the end.
If she cannot make her prayer lengthy, then she should pray two by two, whatever Allah has decreed that she should pray, then when she thinks that she has done as much as she is able to, she should pray Witr at the end, with one rak‘ah.
The scholars of the Standing Committee said: Taraweeh prayer is eleven or thirteen rak‘ahs, saying the tasleem after each two rak‘ahs, and praying Witr at the end (with one rak‘ah) is referable, following the example of the Prophet (blessings and peace of Allah be upon him). But if anyone prays with twenty or more rak‘ahs, there is nothing wrong with that, because the Prophet (blessings and peace of Allah be upon him) said: “The night prayers are two (rak‘ahs) by two, then if one of you fears that dawn is about to break, he should pray one rak‘ah, so as to make what he has prayed odd-numbered.” Agreed upon. So he (blessings and peace of Allah be upon him) did not specify a particular number of rak‘ahs.
A woman does not have to have memorized the Qur’an in order to pray Taraweeh in her house; rather if she has memorized it, or a goodly amount of it, she may pray with whatever she has memorized of the Qur’an.
If she was not able to memorize enough to help her pray at home, there is no blame on her, or on any man, if they pray-reading from the Mus-haf (printed copy of the Qur’an).
Shaykh Ibn Baaz (may Allah have mercy on him) said:
If there is a need to read from the Mus-haf, for one who is an imam leading the prayers, or a woman who is praying Tahajjud at night, or a man who has not memorized the Qur’an, there is nothing wrong with that.
If there are a number of women in the house, there is nothing wrong with her leading them in praying in congregation. She should stand in the middle of the row, and recite whatever she is able to, and if she reads from the Mus-haf there is nothing wrong with that.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) said:
It is better for a woman to pray in her house, even if there is a mosque in which Taraweeh prayers are held, and if she prays in her house, there is nothing wrong with her leading other women in the house in prayer. In this case, if she has only memorized a little of the Qur’an, she may read from the Mus-haf.
It is better for her to pray Taraweeh at home, but if praying in the mosque is more motivating for her and helps her to focus better, and if she prays at home she fears that she may neglect her prayer, then in this case the mosque may be better.
And Allah knows best.