I don't hate "Mama's Song" at all. I just think it's not remotely the best single choice they can make.
There's a great likelihood for Carrie to perform "Blown Away" at the Grammy's if you ask me, after all, it's the most likely song to be nominated. Or maybe a cover. I think it's rare for anyone to single a genre-specific song on the Grammy's in lieu of the nominated work. Even Lady Antebellum performed "Need You Now" twice as a medley in the other year. I also feel it's rare for people to perform current singles which are not lead singles as well:
ADELE performed "Rolling In The Deep" instead of her current single "Set Fire To The Rain";
Rihanna performed "We Found Love" instead of "Talk That Talk";
Shakira performed "Hips Don't Lie" instead of whatever she was releasing at that time, possibly "Illegal", etc.
There's also the possibility of a medley a la the aforementioned Lady A one, and the Taylor Swift with Stevie Nicks one, or the Madonna and Glorillaz one with "Feel Good Inc." and "Hung Up".