How to deal with Toxic Parent and living environment without the obvs solution of moving out of the house?

have you tried talking to your father about this my friend?

what about family members like uncles/aunts/grandparents

are they aware of the situation?

Try to keep your father away from your mother most of the time, do some fun activities with your father, either you will understand him or change him.

Btw in the meantime tell your mother that you are their for her and will do your absolute best to keep the family together without hurting anyone.