Say that I have a wine that still contains a substantial amount of sugar. If I start the process of converting the wine to vinegar by exposing it to oxygen, will the sugar continue to be converted to alcohol during this process? Or will the sugar remain even as the wine is converted to vinegar?
Simply exposing a wine that was inoculated with wine yeast to oxygen doesn't create acetic acid. You need to inoculate with some acetic acid bacteria as well.
Acetic acid bacteria can ferment both sugars and ethanol to make acetic acid.
I have made red wine before, and I have pulled a gallon of partially fermented wine, inoculated with acetobacter and gotten a decent product.
With a fully fermented wine, it will take more time for the acetobacter to convert just the ethanol to acid. Seeing as you still have some sugar, I'd pitch some acetobacter and let it go from there. Consult your local brew shop for the appropriate bacterial strain.