With regards to the entire earth, yes - the 2nd law does not apply. With regards to a closed system that is NOT dependent upon solar energy (or mass accumulation) - like a watch or car - then the law will apply. We know in these cases that solar energy is actually harmful! At least the faded paint on my old 1962 Fairlane seemed to say sunlight was bad!
But in the case of living organic matter, we know that solar energy tends to be either a good thing (plants), or mutative (cancer in man), which can also create diversity of species (witness the natural skin color of Africans/Asians and Northern Europeans).
As with all scientific laws, it is the scope of the frame of reference that is critical. Application of the laws must take into account what you are looking at.
In your example of your car, the energy clearly caused damage but it still was recieving energy so under a technical definition of the 2nd law wouldn’t it not apply. Its that sort of situation which makes me wonder if the second law wouldn’t be better stated if it required the energy to be delivered in some form of an organized manner. Since our everyday experiences show us that unorganized energy tends to be destructive (i.e. it faids the paint, causes mutations, lightning, tornadoes, and etc).
Of course the 2nd Law applies to the earth! Just as it applies to a refrigerator, even though it exchanges heat with its surroundings. In these cases, the 2nd Law says that any decrease in the entropy of the system must be compensated for by an increase at least as great in its surroundings.