بسم الله الرحمن الرحيم و الصلاة و السلام على خير المرسلين
The permessibility for women to perform I'Tikaf at their Home's Masjid is allowed by the Hanafi Madhab , some of the Maliki Madhab scholars and was stated in one of the narration from Imam Al-Shafi'e ( rahimuhum allah). This ruling is based on the following:
The prophet ( صلى الله عليه و سلم ) said to Umm Hamid "I know you like to pray with me but For the woman to offer her prayer in her chamber is of greater merit than to offer it in her courtyard, in her courtyard than in the mosque of her people, in the mosque of her people than in the congregational mosque " [ Sahih Ibn Khuzaimah: 1689]
It is proven that the Salaa of the woman is better to be performed at her house and soshould be the I'tikaf.
'Aisha (Allah be pleased with her) reported that when the Messenger of Allah (صلى الله عليه و سلم) decided to observe i'tikaf, he prayed in the morning and then went to the place of his i'tikaf, and he commanded that a tent should be pitched for him, and it was pitched. He (once) decided to observe i'tikaf in the last ten days of Ramadan. Zainab (the wife of the Prophet (صلى الله عليه و سلم )) commanded that a tent should be pitched for her. It was pitched accordingly. And some other wives of Allah's Apostle (صلى الله عليه و سلم) commanded that tents should be pitched for them too. And they were pitched. When the Messenger of Allah (صلى الله عليه و سلم) offered the morning prayer, he looked and found (so many) tents. Thereupon he said: What is this virtue that these (ladies) have decided to acquire? He commanded his tent to be struck and abandoned i'tikaf in the month of Ramadan and postponed it to the first ten days of Shawwal.[ Sahih Muslim: Book 6: Hadith 2641]
Al-Imam Al-Iraqi stated in his book " Imam Al-Shafie commented on this hadith by saying: " Based on this Hadith I dislike for women to do I'tikaf at any masjid except the masjid of her house because if she does I'tikaf at the Masjid which is normally visited day and night, the chances of her to be seen and see others i.e. males are big" [Tarh Al-Tathrib Fi Sharh Al-Taqreeb: 4/170]
Ibn Abd Al-Bir Said: " Imam Malik said I do not like women to do I'tikaf at her house Majid and let her do I'tikaf at the Majid of Jama'a ( where congregation Sala is offered). Abu Hanifa Said that let women only do I'tikaf at their house Masjid. Imam Sufyan Al-Thawri said: It is better fir women to do I'tikaf at their house Majid than having it at the normal Masjid" [ Al-Istithkaar Al-Jami'e Li-madhahib Al-Amsaar: 3/399]
On the other Hand, the opinion of the Jumhoor from Shafie, Maliki and Hanbali allow women to do I'tikaf at the normal Masjid Only.
Note: The scholars who allowed I'tikaf to be done at the house have specified that it is in the Masjid of the house. in other words, in the place where the woman set for her prayers to be offered. thus, you need to have such place or room or space set for this reason so you can do I'tikaf in it.
On other note, I believe, nowadays, it is better for women to do I'tikaf at their house Masjid because of the following reasons:
1) Most women do not put on proper Hijab and this causes lot of Fitna.
2) The entrance of women and men always meet somehow, and you always find men or women standing outside standing or talking before entering.
3) The noise that happen due to this especially if the woman has kids with her which will distract whoever is in the Masjid.
That is based on my personal observation, which even happens in normal days anyway. yet, in such occasions it is greater.
If I do not greet back in writing then know I do it verbally because sometimes I am too busy and just want to answer the question.