There is actually little evidence in The Kite Runner that addresses this question. Hassan never mentions his mother, and the whole story of Sanaubar's relationship with Ali, her infidelity, and her desertion of the family just five days after Hassan's birth is only discussed behind closed doors.
Hassan never talked about his mother, as if she never existed.
Amir wonders if Hassan dreamed about her, or
Did he ache for her, the way I ached for the mother I had never met.
We do discover that Hassan once cried for her, after a soldier told her that he had "known" Sanaubar "from behind by that creek over there." In the movie theatre later, Amir saw Hassan
... croaking. Tears were sliding down his cheeks.
Hassan did enjoy experiencing his mother's love later in the story, when she returned to Baba's house, now being tended to by Rahim Khan, and Hassan and his wife. Sanaubar helped to deliver Hassan's baby, Sohrab, and the little boy became close to his grandmother in a way Hassan never had as a child. Hassan and Sanaubar also caught up with the past, kneeling together in the garden
... picking tomatoes or trimming a rosebush, talking.