I’d be surprised if they got rid of the nanny with school aged kids. The nanny’s responsibilities would probably change: help get kids ready for school, breakfast, school run, drive to activities, plan for the activities/sports and pack up the necessary supplies, etc. time commitment would change as well. More part time. Then back to full time in summer. I worked for a family that had school aged kids. And there were lots of other families in their area/at their school that had nannies. There was always someone to grab the kids if needed between the parents. And nannies often exchange numbers to help each other out for emergencies so their kids wouldn’t have to depend on their mom’s lack of social skills. Basically if they keep a nanny and pay that person well, the nanny will make sure the kid is taken care of and mom can fully check out and not take any part in raising their kid.
But let’s be honest, a sick kid getting picked up from school due to sickness is definitely vlog content for the rabid stans to consume so I doubt they would pass up the dramatic rushing out of magic kingdom to get a kid.