Following is my views on your transaction - please correct if needed.
Your mother-in-law is giving you a property with the fair market value of $425,000 and in exchange you pay her $340,000 ($320,000 in cash and $20,000 in building materials used for improvements)
So - you were to receive a gift valued $85,000 or $85,000 / $425,000 = 20% of the property.
Your mother's basis on the property is $340,000 (including improvements).
1. Your mother sells you 80% of the property for $340,000. Her basis on that part is $340,000 * 80% = $272,000.
Her capital gain on that part $340,000 - $272,000 = $68,000
2. Your mother gift you 20% of the property with the value $85,000. Gift is not taxable income for you. Your mother - as a donor - might has to file a gift tax return as the gift is above $13,000 (for 2009) per person per year. However there will not be any gift tax unless her lifetime limit of $1,000,000 is reached.
3. Your basis in the property $340,000 (on 80% you purchase) + $68,000 ($340,000 * 20% - your mother's basis on the gifted part) = $408,000
Let me know if you need any help.