Pete, I agree that a brush is probably in order. Woolite is no stronger than
Ultima ISG.
If the brush does not work, you'll need to test to see if the color has bled into the vinyl itself. A good way to find out is with spray hair. Spray a small amount on a soft towel and work on a very small area of the vinyl. The solvent in the hair spray should remove the staining if it's not permanent.
WARNING: Not recommended to treat the whole seat with hair spray as a cleaner. This is simply a test to see if the stain is permanent.