The mom in 'A Christmas Story' is an important character. She's often dealing with the chaos in the family during the Christmas season. Melinda Dillon portrays her. She's the one who cooks the turkey and tries to keep the family in line, while also having her own little moments of exasperation and humor throughout the story.
In the movie A Christmas Story Christmas, Ralphie's mom is named Mrs. Parker. She plays an important role in the family dynamics and Christmas preparations.
Without more details about the particular new Christmas story, it's impossible to determine who the mom is. It could be a completely new character created for that story, or it could be a reimagined version of a traditional character in a new context.