The sale of the funds cannot be reported on your mother's final income tax return since the funds will be sold after her date of death. The funds will have to be transferred to an account titled to the estate before they can be sold. When they are sold in the estate account then the estate would be required to pay taxes on any gains unless the proceeds are passed through to the beneficiaries of the estate. If the funds are passed through then the beneficiaries would report the gains on their individual tax returns. Another option would be for the funds to be transferred (as distributions from the estate) in-kind from the estate account to accounts titled in your siblings names and SSN's and then each sibling could sell the funds in their individual accounts. Each sibling would then report the sales on their individual tax returns.
To calculate any gains or losses on the funds the fair market value of the funds on your mother's date of death are used as the cost basis (plus any reinvestments since that date). So depending on the cost basis there may not be much gain.
If the amount of income earned by the estate is $600 or more then Form 1041 must be filed. Any income that is passed through to the beneficiaries of the estate is reported on Schedule K-1s (copies are given to beneficiaries to report the income on their individual tax returns) that are filed with the 1041.
http://www.irs.gov/pub/irs-pdf/f1041.pdf
http://www.irs.gov/pub/irs-pdf/f1041sk1.pdf
Enrolled Agent
EA, QPA, CHFC, CEBS, CLU - 30 years experience providing financial advice