The law with regard to co-operative societies differ from State to State. Hence it is not possible to express an opinion without knowing the State in which the property is situated. However I give my general observations which may be subject to correction depending on the State.
From what you have written I presume that your father died before your mother. If so you should have produced his Will before the Society soon after his death and not wait until the death of your mother.
A nomination and a Will can have different connotations.
A nomination is not a Will and the latter will prevail over the former. A nomination is a direct instruction to the Society as to whose name the property should be transferred in the event of the death of the nominator. It does not necessarily imply that the nominee will be the owner of the property. But since it is directly handed over to the Society during the lifetime of the nominator, the Society need not seek any other evidence to act on it at the appropriate time.
A Will declares who shall be the owner of the property on the death of the testator. The property cannot go any further. But since a Will is not handed over by the testator to the Society during his lifetime the Society cannot act on the Will straightaway. The Will will have to be authenticated by obtaining a probate on it from a competent authority. The law on probate varies from State to State. Probate is not required in some States. But still a Society may play safe and not act on a Will without a probate.
If the Will of your father was in your own favor, how did the property pass on to your mother after your father's death. If your father had nominated your mother in the books of the Society, but bequeathed the property to you, why did you not claim the property from your mother (the nominee) even before her death on the basis of the Will?
Probably you did not disclose the Will of your father at all until the death of your mother. As your mother was only nominee of your father and it was not bequeathed to her, she was only holding the property as a nominee of your father and she had no right to give any further nomination. Thus her nomination of your name is not valid.
You have unnecessarily complicated the whole thing. Under the circumstances the Deputy Registrar would be afraid of touching your case even with a pair of tongs. Either you can make an attempt to obtain a probate on the Will and produce it before the Society or resort to a court of law.
The inaction of the Society may be either due to their lack of knowledge or because of their knowledge of things. Did you ever make an attempt to sit down and discuss the matter with the Secretary. My advice would be you try to withdraw the Will and request the Society to act on the nomination only. Once the Will has come into the knowledge of the Society they can refuse your request. If they agree you can keep the Will with you for production just in case of a counter-claim. Please note that probate on Will is also subject to stamp duty in States like Maharashtra.