The rental house would create a sale for you, your sister and your mother. Because this was a gift, your cost basis would be the same as your mother's cost basis split between you. Mortgage payoff is not significant on the tax return. The mortgage interest and property taxes would be part of the rental activity on the tax return, however not part of the sale.
The original purchase price of the rental house would have been used for depreciation, so any payoff is not a consideration.
Cost basis is what was paid for the rental house, plus purchase expenses, plus capital improvements, minus any depreciation that was allowed (whether or not deducted) on the property while it was available for rent. This is how you would arrive at the full cost basis (review the next paragraph as well for possible inherited value portion).
Easiest & Logical method: Your mother could choose to report the entire sale on her tax return since that is where the rental activity has taken place. This would be the simplest and each of you could pay your portion of the tax bill to her if you choose to do that. She technically inherited half the house when your father died assuming it was jointly owned while he was alive. This means she would have a cost basis on the date of death of half the fair market value on that day and then her actual cost basis (shown above) for the other half. In TurboTax you could add this value difference in the sales expense to account for the reduced gain.
If each of you reports the sale equally, the cost basis and depreciation would need to be reflective on your mother's return which is more labor intensive for her to report only her portion.
If the property was located in Maryland (MD) and that is not your resident state, you must file a nonresident return for MD, They will want the tax dollars for the gain received on the sale of property in their state. It's not likely it will be refunded to you. Since Washington (WA) doesn't have income tax, there is no return to file for your resident state.
This is NOT an inheritance and inheritance rules for sale will not be used since the properties are placed in your names (you and your sister) before her death.
The home sale, for her will be a sale of her primary residence assuming she meets the eligibility requirements. For both you and your sister it would be a sale of an investment if neither of you lived in this house as your personal residence.
The house would likely belong to your mother automatically after your father's death. Your portion again is a gift if the house was put into your names (not just profit splitting), after the death of your father. It seems you are saying that this event took place after the death of your father.
There are questions such as whether a gift tax return was filed or if the value was high enough to meet the filing requirements. This pertains to both houses. And gift tax is beyond the scope of this forum.
Please update here is you have more questions.
[Edited: 03/28/2021 | 8:09a PST]
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