Is my mother's use of a stone for wudu and purification valid in Islamic law, given her psoriasis prevents her from touching water?

If your mother fears harm from using water, it is permissible for her to perform tayammum (dry ablution) for all acts requiring ritual purification. Tayammum is performed with "pure earth" (al-sa'id al-tayyib), and scholars have differed on its exact meaning. The Hanafis held that it refers to dust and whatever is of its kind, while the Malikis believed it encompasses everything that rises from the earth's surface as part of its components. The Shafi'is and Ahmad, however, restricted it to dust. If the stone has dust clinging to it, her tayammum is valid by consensus. Otherwise, it is not valid according to the majority, and she must repeat the prayers, though it is valid according to the Malikis.