Oh gosh, I didn't even realize the recipe called for so much vinegar! Yes, you definitely need to replace the liquid. Let's see...it's hard to tell what kind of liquid would work best without knowing what the end product is supposed to taste like. You could use water for some, orange juice, buttermilk, yogurt thinned with milk...
Brown sugar does react with baking soda, to the best of my knowledge. Baking soda is usually the leavener in cookie recipes and brown sugar is often the primary acidic ingredient. Since the recipe is for "bars" the brown sugar may be enough with the addition of a little more acid (a few squeezes of orange juice) if the bars are supposed to be dense; if they are supposed to be cakey, something else is probably needed.
The cherry pie filling may be acidic too, since cherries are naturally acidic.