It may depend on what state you live in. If you live in a community property state or if your father was the sole owner, your mother's basis would be FMV at your father's death. If they lived in a non-community property state and held the property as Joint Tenants with Right of Survivorship, your father's half only would be stepped up. The basis to your sister was your mother's basis. But when your sister died, all of that became irrelevant and the basis for your mother became the FMV at date of your sister's death. When she gifted it to you, there was no change: your basis is the same as your mother's was, which is the FMV when your sister died. Gifting appreciated property near life end is usually a bad idea, unless it is a charitable gift.
It is usually better to die with appreciated property in order to take advantage of the free step up in basis.
