In this case, since the property in question was self-acquired by your mother’s father, the rules of succession under Section 8 of the Hindu Succession Act, 1956 would apply. Let’s go step by step.
Your mother’s father died in 1955, that is, before the Hindu Succession Act, 1956 came into force (it came into effect on 17 June 1956). Therefore, the succession to his self-acquired property would not be governed by Section 8 of the Hindu Succession Act, but rather by the old Hindu law (Mitakshara law) that was applicable before 1956.
Under the old Hindu law (before 1956), when a Hindu male died intestate (without a will), the property devolved upon his sons, and the daughters had no right to inherit, unless there was a specific regional or customary law providing otherwise. Therefore, if your mother’s father died in 1955, the property would have devolved only upon his son (your mother’s brother), and not upon the daughters, because the law giving equal rights to daughters did not exist then.
So, the civil court was right in holding that Section 8 of the Hindu Succession Act is inapplicable, because the succession opened before the Act came into force. The Act does not have retrospective effect.
If, however, there was clear evidence that the property was not divided and that your mother’s father’s estate remained joint and unpartitioned till after 1956, then one could argue that the succession opened later — but from the facts you shared, that does not appear to be the case.
Therefore, your mother would not be entitled to a share in her father’s self-acquired property since her father died in 1955, before the Hindu Succession Act, 1956 came into force. The right to claim a share under Section 8 would have applied only if her father had died on or after 17 June 1956.
In short, under the law prevailing in 1955, only the son inherited, and the daughters were excluded from succession.