All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The awrah (private parts) of a woman during prayer includes her entire body except for her face and hands. It is permissible to uncover her face and hands during prayer. In the Shafi'i school of thought, it is mentioned in the book "Asna al-Matalib" (Vol.1/P.176): "The awrah of a free woman during prayer, and in the presence of a non-Mahram even if outside of prayer, is her entire body except for her face and hands, both the back and front, up to the elbows."
It is important to note that permissibility does not imply obligation. If a woman prays while covering her face, her prayer is valid, although it is disliked to cover the face during prayer. In "Mughni al-Muhtaj" (Vol.1/P.400), it is mentioned: "It is disliked to pray in a garment that has images... and for a man to pray veiled, and for a woman to pray veiled." The dislike for covering the hands is less, as some scholars among the Hanbalis have stated that it is obligatory to cover the hands during prayer.
In conclusion, if a woman covers her hands during the prayer, or if the prayer garment drapes over her hands during the prayer or while sitting in the Tashahhud, there is no obligation for her to uncover her hands, and her prayer is valid. And Allah the Almighty knows best.
