You are correct. If your mother reports the entire sale of the rental property, then you and your sister do not report any sale. Do not duplicate the sale.
For the Maryland (MD) return, you should file for a refund, however your mother will file for the entire sale on the MD return just like the federal. It's important to be consistent on both returns. The refund should be automatic, however they may require an explanation so you should be prepared to show and explain that your mother filed for the sale since she is technically the owner with your names listed as a convenience.
The primary residence, because it was placed in your names before death would be considered a gift (no inheritance rules apply). It's important to follow through with the gift tax return by checking with an estate attorney. The home sale has different ramifications because of the home sale exclusion.
Since the home is in three names then the cost basis will have to be split three ways, the sales proceeds and sales expenses would also have to be split. In this scenario the sale would be reported by each of you because only your mother would be entitled to the home sale exclusion. You and your sister would pay tax on any capital gain.
Gifts Holding Period— Your holding period includes the time the person who gave you the gift held it.
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