This doesn't apply to you. Cost basis and date of acquisition will only come into play when you sell the stock. A capital gains distribution is an amount that you have received on the value of the stock, but the stock is still an asset that has not lost it's basis. So actually you are correct in reporting all of the $53.37 as a capital gain, which will receive a more favorable tax treatment on your return since it is a long-term gain (more than one year held).
But you do want to know the acquisition date and the cost basis for when you do sell the stock. You certainly will not want to report zero as the stock's basis because that would make the entire amount taxable. Your cost basis was the value of the stock when you inherited it. However, your acquisition date is when your mother purchased it.
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