Is sleeping at one's aunt's house due to the impurity of one's own home considered abandonment and disobedience toward one's parents, and what should be done about it?

Obeying one's mother is obligatory, and disobeying her is a grave sin. Therefore, you must obey your mother if she prevents you from going to live with your aunt. Do not think that your helping her with housework or responding when she calls is a favor; rather, she has a favor over you. Al-Bayhaqi narrated from Sa'id ibn Abi Burdah that a man carried his mother and circumambulated the Kaaba with her, whereupon Ibn Umar said: "Not even for a single groan." As for prayer: The basic principle regarding a place is its purity unless you are certain of its impurity. Impurity can be cleansed by pouring water over it, or by praying on a barrier that comes between you and the impurity.