You and Bob need to be on the same page when it comes to the values shared with your kids and the manner in which they are parented. Just because you believe in a different form and approach when it comes to discipline, that does not mean you are undermining his approach or that your approach is faulty. These are your kids and you need to be their advocate. That does not mean surrendering your role as disciplinarian to Bob. Getting kids "to mind" and punishing them when they don't is not productive discipline or loving parenting.
I'd like you both to read and discuss the following two books, as they regard parenting and discipline: Loving Your Child Is Not Enough: Positive Discipline That Works, by Nancy Samalin and Why Parents Disagree, by Ron Taffel. If Bob will not even entertain another approach to discipline other than his own rather harsh methods, you need to both see a family therapist about this matter. If he won't see a therapist with you, see one alone to discuss this matter and your partnership and parenting relationship with Bob. Your kids deserve the most loving, supportive form of discipline possible and I am asking you to be courageous enough to give it to them.