The answer to your question depends on whether or not a "life estate" was legally created at the time the property was gifted in the 1980's. (Your description sounds like it may have been.) This web reference explains a life estate: http://real-estate-law.freeadvice.com/real-estate-law/real-estate-law/life-estate.htm
If a life estate was created, and you (& your siblings) are the remainderman, since you sold it after her passing your cost basis when you sell it is its Fair Market Value ("FMV") at the time of your Mom's death. This is called a "stepped-up" basis.
But if no life estate was created and the property was simply gifted by your Mom to her children, your cost basis (if you sold it at a gain) would be your Mom's original cost, plus any capital improvements made to the property over the years. You can find more details (on sale of gifted property) here: https://www.irs.gov/help-resources/tools-faqs/faqs-for-individuals/frequently-asked-tax-questions-an...
One of the requirements for the capital gains exclusion is that the seller must have lived in the home as their primary residence for at least 2 of the 5 years leading up to the date of sale, so it appears the exclusion would not apply in your case.
Consult an attorney if you're not sure about any aspects of the situation.
**Answers are correct to the best of my ability but do not constitute tax or legal advice.
