Town Reset?

DivinylsFan​  If you reset the town while kids are at school, then of course they'll be reset to home and not be attending school at that moment.  NRaas StoryProgression should push them to go back, but it can take a couple sim-hours, depending on how many sims need to be pushed back to work or school.

For the overcrowding, you could put down a second school, and reassign some sims to go there (NRaas > MC > Sim > Intermediate > Career > Choose School).  Newly-aged-up sims should start choosing the other school at least some of the time too, especially if it's closer to where some of them live.  The SP Career add-on allows for private schools at various other rabbitholes, so you could for example have some sims attend art school at the theater, or something like that; I don't use the feature myself.

As for why the car is getting stuck on the lot, is this the default version of SV or a new one?  An edited map might have broken routing, but the original is pretty solid.  Still, you could replace this rabbithole with one from another world if you want.  You could also edit the lot if you notice a particular spot that's a problem.

This mod is also helpful:

https://modthesims.info/d/568897/additional-entry-and-exit-routing-slots-to-reduce-door-crowding-schools-university.html

Note that you'll need to widen the path around the back entrance/exit to make it usable, but that takes thirty seconds.  And you'll need to run another MC reset afterwards if you're not starting a new save.

As for MC resets in general, I always try to run them in the middle of the night, or before the workday starts, to avoid issues with sims leaving work/school/other activities.  If something is stuck in the middle of the day, you can reset only that lot, or only the object on the lot.  For example, in this case, you could click the ground of the school lot and select MC > Object Reset > [car name].  If that doesn't work, run a DebugEnabler reset on the car itself.