Yes, it's taxable and no, it's not an inheritance, it was a gift 15 years ago, and the rules are different.
The problem (from a tax point of view) is that your mother gave you the house 15 years ago. When you get a gift, your cost basis in the gift is the same as the giver's cost basis. So the simple answer is that, your cost basis is 1/3 the price your mother paid for the house. If the $80,000 now is more than 1/3 the original cost, the difference is a taxable capital gain.
But, it's way more complicated than that (unfortunately).
Your mother's cost basis as of the date of the gift will depend on if she previously owned it in common with a spouse who died first,and also on any improvements she made over time.
Example: your mother and father bought the house for $40,000. Over time, they made $10,000 of improvements. At the time of your father's death, the house was worth $100,000. Your mother's half of the cost basis is now $25,000. Then inherits half of the value of the house on the date of her husband's death. That's $50,000, so her adjusted cost basis is now $75,000.
Then, she gifts the house to her three children. Each child has a cost basis of $25,000. In the last 15 years there were $10,000 of new improvements. Now each sibling's share is $25,000 + $3,333 = $28,333. If you receive an $80,000 buyout for your share, you have $51,667 of taxable gains, taxed at the long term cap gains rate.
A further problem is that, if you are audited, you won't get the benefit of anything you can't prove. So you need to collect documentation of:
•How your mother acquired the house (buy, inherit, gift) and the cost she paid.
•If she acquired it with a spouse, you need to know the market value on the date of the spouse's death. (A local real estate appraiser can give you a retroactive estimate.)
•The cost of any long term improvements to the home made over the years. Improvements are different from repairs; repairs restore damage to as-was, an improvement extends the useful life of the property or adds value. Improvements only count if they are still part of the property. For example, if the carpets were replaced in 1990 and again in 2010, only the 2010 replacement counts.
•Any negative adjustments to cost basis, such as depreciation taken for business use of the home (home office deduction, use as a rental).
(Note to anyone reading this: there are better ways of transferring property from a parent to children that avoid this tax problem AND protect the asset from the government at the same time.)
There is no way to avoid the capital gains tax. Your gain is not the proceeds, is the the difference between the proceeds and your basis. You will owe that on your tax return no matter what.
You can lower your tax bill by making tax-deferred investments into a IRA if you are working (up to $5500, but possibly less if you are covered by a retirement plan at work). You can also lower your tax by making donations to charity, or paying next year's property tax bill early, but those tax strategies are the same for all taxpayers. Any interest you earn on the money while it is in a non-tax deferred account is also taxable. But getting $500 of interest and paying $150 in tax is better than getting no interest at all.
