If your name was on the deed at the time of the sale, then you and you alone sold the house. 100% of the gain from the house is taxable income to you, and only you. You will report the sale of the house on your tax return. Your cost basis in the house it it's FMV at the time of your mom's passing, and not at the time you inherited it and put it in your name.
The proceeds you shared with others is considered a gift. None of the recipients of your gift have to report it on any tax return. However, if the amount of your gift to any one recipient was more than $14K in a tax year, then you the giver of the gift have to file a form 709 Gift Tax Return with the IRS. There will be no additional tax imposed on you for the gift provided is was under $5.2M. But if it was more than $14K then you do have to report it to the IRS.
The TurboTax program does not include the IRS Form 709 and can not be used for filing the gift tax return.