I think there's one other thing missing from the discussion.
If your father retained a life estate (the right to live in the home as long as he was alive), then you inherited the entire house with a stepped up basis. That would mean you had no taxable capital gains, as long as you sold the home at or below the FMV on the date of your father's death.
If he did not retain a life estate, then you inherited half the house with a stepped up basis, but the other half of the house (the half gifted to you in 2008) has a cost basis equal to half your father's cost basis in 2008, which is calculated from the purchase price, cost of other improvements, fair market value when your mother died, and whether or not your parents lived in a community property state.
Now the key is, a life estate can be in writing in the deed, or it can be implied by the facts and circumstances even if is not in writing. If you can show by facts and circumstances that your father retained an implied life estate, your tax position suddenly becomes much simpler. This is another reason to consult a professional tax and legal advisor.
