As per the Indian Succession Act, 1925, if a Hindu Female dies without writing a valid will then her own wealth will be distributed as under, in this order -
The son and daughters and the husband.
The heirs of the husband.
The mother and father.
Heirs of the father.
Heirs of the mother.
Property acquired from Husband -
If the women has acquired any property from her Husband, in that case the first right will be of the heirs of her husband, in case of absence of her sons or daughters.
Thus, the question to be answered here is whether the maternal grandmother acquired the said house property from her 2nd husband or it was her own property to begin with. Given the fact situation it does seem to be the case that since the house was bought in her name, it can be safely assumed to be MGM’s self-acquired property even if it was bought by her husband. Section 27 of the Indian Succession Act, 1925 clearly states that as far as succession matters are concerned, the law will not discriminate between those related to the deceased person by full blood and those related by half blood. However, it is important to note that such a relationship must be with the deceased, and not the spouse of the deceased. 
Now, the question of inheritance with respect to this house property will be the same for the aunt and the mother, since both of them are MGM’s daughters. Therefore, her property will be divested among her daughters, equally. However, here, the aunt seems to have a larger share in terms of having the electricity bill and other meters in her name. But after MGM’s death, the proceeds from her property must be divided equally among her heirs i.e. both her daughters.
With respect to the second issue of availing the pension, the family pension scheme is available only to the dependants of the deceased i.e. the second husband of MGM. It is to be noted that the mother (MGM’s first daughter) is not a dependant of the deceased, and is therefore automatically ineligible to receive the pension amount. Moreover, married daughters are ineligible for availing the pension amount under the said scheme.
Therefore, only the aunt is eligible to get the pension on behalf of her own deceased father (provided she is still unmarried).
Indian Succession Act, 1925
See Scheme for Payment of Pension to Central Government Civil Pensioners, Available at CS No 4, UO No 1(7) 1(2000)/TA/377