Translation:For my salad, I added vinegar to the dressing.
Does anyone else feel let down by the revelation that the French word for "salad dressing" is simply sauce? Consider how French prides itself upon its precision, its panache--then realize that even plebeian Spanish has a nice, manly special word for the stuff the veggies are dipped in! Even adding "vinaigrette" can't make up for this shocking lack of imagination. Perhaps the Académie would be persuaded, in the tradition of "camping" and "shampooing," to add "dressing" to their dictionary or better still, "le wishbone" in the tradition of the proper-name originated "le sandwich," "la bru," and even "la poubelle." ;-P
I think the answer is in the other example you gave. Note that in "biscuits au chocolat" the "biscuits" is first and the "chocolat" is second. I believe the way it works is that the "main thing" so to speak comes before the "à" and the secondary is after, so "vinaigre à la sauce" wouldn't be "vinegar sauce", it would be "sauce vinegar", which isn't a thing as far as I know. Try to think of the "à" as "with" in this context.