When your mother gifts 20 cents to your father, the income on sale of such land will be still assessed in her hands, attracting the provisions of Section 64(1)(iv) of the Income Tax Act.
When your mother gifts another 20 cents to you, assuming that you are a major son, the income thereon will be assessed in your hands only. When you sell the property, the cost of acquisition of the property by your mother will be the cost of acquisition for you also and the indexation will also be applied from the year in which she acquired the property though the property is transferred to you only now.
As there will be two assets on which capital gains will be worked out in your mother's hand as well as yours, you can consider investing in capital gains bonds u/s 54EC upto Rs 50 Lakhs each. After a lock in period of 3 years, the money will be available to you to use in the manner in which you would like to invest.