I dont remember any real backstory wrt her mum in the book and the Townes story was very much based on him beher first 'crush', he never came to moscow.
ie lots of dramatic licence but it doesnt matter, i think they really captured the essence of her story.
The following is Tevis' description of her playing at the high school pure imagery but i dont think it could have been done better.
^Her mind was luminous, and her soul sang to her in the sweet moves of chess. The classroom smelled of chalk dust and her shoes squeaked as she moved down the rows of players. The room was silent; she felt her own presence centred in it, small and solid and in command. Outside, birds sang, but she did not hear them. Inside, some of the students stared at her. Boys came in from the hallway and lined up along the back wall to watch the homely girl from the orphanage at the edge of town who moved from player to player with the determined energy of a Caesar in the field, a Pavlova under the lights. There were about a dozen people watching. Some smirked and yawned, but others could feel the energy in the room, the presence of something that had never, in the long history of this tired old schoolroom, been felt there before.
What she did was at bottom shockingly trivial, but the energy of her amazing mind crackled in the room for those who knew how to listen. Her chess moves blazed with it. By the end of an hour and a half, she had beaten them all without a single false or wasted move. ^