Because you receive a stepped-up basis for the home (equal to its value on the date of your mother’s death), you may have no gain from the sale if it occurs soon. If you sell it for less than this basis, you have a capital loss that can be reported (assuming neither of you uses the home as your personal residence). If you have a gain, it is taxable (no home sale exclusion applies because you did not own and use the home as your principal residence for the requisite time period).
A husband and wife who are required to live apart from each other by the terms of a decree of separate maintenance. Payments under the decree are deductible by the payor and taxable to the payee as alimony.