Combine first 7 ingredients in a large glass or ceramic container. Cover and refrigerate overnight. Drain and rinse in 3 cold water baths.
Combine carrot, cauliflower, celery, green beans, squash, and water to cover in a large stainless steel saucepan. Bring to a boil. Reduce heat; cover and simmer 15 minutes, stirring frequently. Drain well.
Combine vinegar, sugar, 2 cups water, and spices in a stainless steel stockpot; stir well. Bring to a boil. Add reserved vegetable mixtures, mixing well. Return to a boil. Reduce heat; simmer 10 minutes, stirring frequently.
Pack relish into hot sterilized jars, leaving 1/2-inch head space. Remove air bubbles. Cover at once with metal lids, and screw bands tight. Process in boiling water bath 10 minutes.