Parents own joint property and are separated can father claim share

My parents own 50% share each of our house with no loans pending. My parents are separated, my father lives in a rental house somewhere in the city with a woman. He has a 2 year old child with this woman. My mother lives in our house. The deed of the house does not state which part of the house or plot is the mother's or father's. My question is - can my father sell his share of the house without my mother's consent? Under what conditions can he sell his share of the house?