I added wine to my sauce, it will be cooked for about a day before eating. Will alcohol show in a UA?

Using wine (low alcohol content) and cooked over a long period should remove all of the alcohol content. Additionally, the proportion of alcohol will be too low to register on a standard urine alcohol test (uses cutoff of .02). Even if some alcohol survived and the UA tested for EtG you should still be safe, once again due to the low quantity.

You are thinking along the right line however, as the alcohol content of a food additive (vanilla extract, as example) stirred in the mix and then baked for 30 minutes will retain 35% of the original amount of alcohol. Many of the food additives have alcohol content higher than hard liquor.