Is my re-reading of Al-Fatiha and praying aloud in front of my mother to ensure proper recitation considered hypocrisy (riya’)? And does daily doubt in prayer make me one of those who doubt excessively?

The treatment for obsessive thoughts (waswas) is to completely disregard and ignore them. If Satan instills doubt in a worshipper, making him think he prayed one rak'ah instead of two, or prostrated once instead of twice, or he doubts the correctness of his recitation and articulation, then he must not pay attention to these whispers and should continue his prayer. Your prayer in the presence of your mother is not showing off, but it does not cure the obsessive thoughts; their cure is to cut them off and ignore them.