My father has uncle and this person is married to his mother (My grandmother) and he married my mother's grandmother and divorced her. He is living in our house now. Is it inviolable when he looks at my mother? Is it inviolable to live with us in the same house? I appreciate your attention.

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

We found that is lawful for the man to dwell with you, because he is unmarriageable person for the whole family. He is uncle to you, because he's your father's uncle and uncle of the father is the uncle of the father's children.
At the same time, he is just like a grandfather to your mother, since he married her grandmother and consummated married life with her. Her mother is her big "RABIBA" (step-daughter), and she is his little "RABIBA", and Allah Almighty prohibited the "RABIBA" Saying: {And your step-daughters under your guardianship, born of your wives to whom you have gone in - …."} [4:23].
Allah knows best.