What preposition is best in this sentence?
I would rather you arrived on time to school.
I would rather you arrived on time for school.
What preposition is best in this sentence?
I would rather you arrived on time to school.
I would rather you arrived on time for school.
Whilst both of your examples are grammatically correct, in my opinion, the more natural phrase might be:
I would rather you arrived to school on time.
I think the nuances between your two examples are dependent on how to interpret the meaning of the word school, for example:
to school
Uses school in the noun sense, implying arriving on time at the building.
for school
Uses school in the verb sense, implying arriving on time for schooling.