You’ve got two options that I can think of.
The easy route is to conform to the paperwork. You report the entire sale as if you owned 100% of the home, and you pay 100% of the capital gains tax. Then, you make a gift to your sister in the amount she is owed (her share of the house minus the taxes). If the gift is more than $17,000, you would have to file a form 709 gift tax return, but gift tax is not actually owed unless your lifetime total gifts are more than $13 million. The purpose of form 709 is to keep track of large gifts against your lifetime limit. The recipient of the gift never pays gift tax.
The other route would be to file based on what actually happened, that you and your sister each owned half the house. Each of you would report half the sales proceeds, half the basis, and pay half the capital gains tax on your own tax returns. The IRS may send you a letter asking for more information as to why the sales proceeds that you reported don’t match the 1099S. You would reply with a letter and other proof, showing that you only inherited half the house, that the probate court made an error on the title, And that your sister reported and paid capital gains tax on the other half of the sale. You would probably have to include your sister’s name and address, so the IRS could look up her tax return and find the matching income.
I think this is less unusual than it seems, sometimes when there are more than one owner, only the first owner’s SSN will be on the 1099 anyway.
