Am I obligated to repeat the prayer, or will I be sinful if I am unable to recite the Fatiha and a short surah completely when praying in congregation with my mother, who recites quickly, knowing that she will get angry if I pray alone?

Congregational prayer is, according to the preponderant opinion, recommended for women. It is better for the questioner to pray with her mother, and it entails greater reward, if the mother performs the prayer correctly. The questioner should try to speed up her recitation in prayer without compromising thoughtful reflection, and she should frequently remind her mother, gently and kindly, to slow down her recitation. Reciting a surah after Al-Fatihah is recommended, not obligatory. As for Al-Fatihah, it is a pillar in every rak'ah, and bowing before completing it is not permissible.