That is exactly the correct way to report this particular car expense situation. The two Schedule Cs need to be completed without reference to each other.
If each business were seen as being totally unaware of the existence of the other, then all mileage put on the car that is not for that business must be assumed to be personal.
In the final analysis, what matters is that each business is allocated its share of the total mileage for the car during the entire year, and the sum of the car expenses for the two businesses does not exceed the actual business use of the car.