1. How did your father granted his home to your mother. Is it through WILL or Gift Deed in your mother's favour while he was alive.
2. If it is assumed that he had written a WILL, the same is valid if it is authenticated by 2 witnesses.
3. Does the property now stand in your mother's name or still it continues to be in the name of your deceased father.
4. Whether the property is your father's self-acquired property or ancestral one.
5. If your father had died intestate and if it were to be a self-acquired property, then your mother and her children(two brothers & two sisters) i.e., each one will be eligible for 1/5th share.
6. If the ownership is in your mother's name,based on the relinquishment deed executed by all her children in her favour, she can execute a WILL bequeathing the property to anyone or to all 4 children, provided your father's WILL is not available or else she can bequeath her share(1/5th) to any one or to any child/children or all 4 children..
Based on the answers to the above queries, the correct opinion can be given..