1) In case of an inheritance, the cost of acquisition should be the cost at which your father had bought the property.

2) LTCG should be computed as the difference between net sale proceeds and the indexed cost of acquisition and improvement. And this will be taxable in the hands of each of you, to the extent of the individual share of each legal heir

3) You can each avail an exemption from LTCG tax to the extent of each individual share of LTCG by reinvesting the LTCG in one new residential property situated in India, within the specified time—within one year prior to the sale date, or two years from sale date, or within three years of the sale date for an under-construction property.

1. when sale proceed is divided among legal heirs then each are liable to pay capital gain tax to the extent amount received.

2. for the saving of this tax you should invest the sale proceed either into tax saving funds or reinvest into another immovable property,

And what if only my mom buys another house with the entire amount?

in this case no capital gain tax will be levied. because in this condition it shall be presumed that you have relinquished your interest/share in favour of your mother.

If on an agreement among you three, your mother sells the property and utilizes the entire sale consideration towards the purchase of another property, then she is exempt from long term capital gains tax. You both need not pay any tax for the property sold and another property was bought of the entire sale proceedings of the previous property. .