Is second secret marriage in Islam legally valid under sharia law

Sir,I am a Muslim housewife. My parents have been married for past 50 years now. My deceased father had done second secret marriage when I was 17 years of age. He has 2 sons in that relation. My mother has 3 daughters.I am the youngest one. Its been 6 months that he passed away. He had kept both families separate and there were no discussions about each other from both sides. We first saw them on his funeral. My question is , is that marriage legal under the shariah laws,considering the fact that my mother was unaware of this ? Is there any law that permits us to keep the house which we are living in for the past 32 years? Let me also add that my father has sold his property of 22cents land in native for 35laks and made them a house which is in their mothers and his name. Our house is solely on his name. Till his last breath he was with my mother.What security does the Indian Muslim Law give us three girls and ailing mother in this regards? Kindly tell us how to proceed from here regarding the property