All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.
We did not find this hadeeth to which the lecturer referred in any of the books and references available to us; we do not believe that it is an authentic hadeeth, especially if it suggests that it was recommended for this specific woman mentioned in the hadeeth to perform the prayer at her house and not Muslim women in general.
In fact, this plainly contradicts the authentic hadeeth that reads, "Do not prevent your women from going to the mosques of Allaah." [Al-Bukhari and Muslim] The version cited by Abu Daawood reads, "Do not prevent your women from going to the mosques; but their houses are better for them (for praying)."
It is well-known that Muslim women are allowed to go to the mosques as long as there is no fear of fitnah (temptation, tribulation) and they adhere to the enjoined provisions governing the woman's interactions outdoors such as observing the hijab and avoiding wearing perfume and incense, especially if attending the prayers at the mosque brings about other benefits such as attending religious lessons or sermons or the like. Nevertheless, it is better for them to perform the prayers at home.
Allaah knows best.