Q. Could I use the home sale exclusion to help lower some gains tax?
A. No, since it was not your home.
But, you (most likely) don't really have a taxable capital gain.
The usual rule, for a gift (when your mother put you on the deed), is that the recipient's basis is the giver's basis (what you mother paid for it). But there is an exception for the gift of her home, where she retained the right to live there ("life estate"). "If your mother gave away an asset and keep a life estate in that asset..... the cost basis of the house is "stepped-up" to the value of the house on date of death [IRC 2036]")
More info: http://www.law.cornell.edu/cfr/text/26/20.2036-1
Since the house sold shortly after her death, there is unlikely to be any capital gain. Considering the expenses of sale, there may even be a capital loss. If the house was "investment property" (no significant personal use by you or others, after he death), you can deduct the loss.
A life estate does not have to be explicitly established in the deed. Your mother probably had an "implied life estate." If so, that would give you the stepped up basis. There is case law on this.
