• Share of mother's house after son's death

Mr 'A' died in 2002 leaving behind Wife,2 sons and Mother as Class 1 Legal Heirs. Mr "A'' has some self acquired House property allotted by Improvement Trust and has made no will. In 2010 Mother of Mr.'A' also dies leaving no will. 
Mother had 2 Sons and 4 Daughters out of which both Sons have since expired.
The House Property is not yet Registered.
Wife and 2 Sons of A,that is immediate family members of A have to apply to Improvement Trust for Registration of house which was Allotted to A.

Now the Question is in whose names will the Registered Sale Deed be executed after death of male Mr A
Wife and 2 Sons of A are alive
What will be the status of the share of Mother,will her name be included or not.Mother has expired in 2010.
 
Will the property right of Mother roll back to wife and children of Mr. 'A' or to remaining Class1 Heirs of Mother (2 Decesed Sons and 4 Daughters) As per Section 15(2) of Hindu Succession Act, property should not be allowed to drift away from source through which female heir has actually inherited the property.Else object of Section 15(2) will be defeated and will become meaningless and redundant. So does it means that after death of Deceased Sons Mother, the Mother’s Share in deceased son’s House property would devolve upon remaining Class 1 Heirs of the source,which means wife and children of the deceased son. Else, the Deceased son’s share would ultimately drift away to his brothers and sisters through deceased mother’s route. Is this position correct.

Is it correct to say that under Section 23 of Hindu Succession Act (Special Provision respecting dwelling houses), Mother of deceased son acquired only right of residence in son's house property.Which means as long as she is alive she can live in the house.Section 23 does not give any right of partition to the female heir.Hence as per this section,after mother's death Deceased male's wife and children would be the only remaining legal heirs to the house property. As regards 2005 Ammendment,the said Ammendment came in year 2005 whereas Mr A died in year 2002 at which time this Ammendment was not in force.The Right of Residence of deceased son's mother accrued in year 2002 when he died.Hence the said Ammendment does not apply in this case.Is position legally correct?

Info regarding the house:The Plot was purchased by A from Improvement Trust in Auction and thereafter House was constructed and Mr A lived there.After some time due to Job Transfer Mr A shifted residence to other city but did not give the house in question on rent.Mr A’s parents lived in the house.