In a nonaluminum container, combine seeds, dry mustard, water, vinegar, and wine. Cover. Soak for 48 hours; add water, vinegar, and wine (if necessary, in correct proportions) to keep seeds covered. Stir at least once a day.
Transfer to a food-processor. Add garlic; process until creamy and seed-flecked (about 6 minutes). Add enough water, vinegar, and wine (in correct proportions) to make creamy; it will thicken slightly upon standing.
Transfer to a 2-quart crockery cooker. Cover. Cook on low heat for 4 hours, maintaining temperature of 130 degree F to 140 degree F. Do not simmer. Stir five times during first hour; stir occasionally during remaining time. Press through a fine-mesh metal strainer. Transfer to a nonaluminum container. Stir in remaining ingredients. Cover and store in refrigerator for up to 6 months. After 3 to 4 weeks, the flavor mellows and improves. Makes about 1-3/4 cups.