I worked for the public school system before re-opening this year, and cabs are contracted to transport some students - usually those who either have special needs or who have been deemed 'homeless' and have moved out of their school's area, but they are provided transportation to continue at the school and not have more disruption in their lives. (not that either applies here, but they are the common reasons for a cab.) The driver is consistent, so is like a bus picking up every day.
That said, I don't give up my time lightly, and would already be over waiting for someone to show up. If you tell me you need me at 7, you'd better be here at 7, KWIM? I think this family would be a hard pass for me.
Edited to add: If she called me 'young lady', I might just ask for pick up right then. That just doesn't hit me well. It seems very condesending.
