T.N.
When you count to 3, you are training her to delay obeying you, so I strongly agree with the immediate obedience method that your husband prefers. The parenting classes I have taken have suggested that as well.
Along those lines, I HIGHLY recommend taking Love and Logic Parenting classes. I am seeing remarkable positive changes in my toddler's behavior since applying the principles/ideas I've learned through attending Love and Logic classes. They are actually based out of Colorado. You can call the Love and Logic company at 800-588-5644 to get the contact info for people who teach classes in your area (I just called and a real person answered right away and was very helpful).
The Love and Logic approach is all about tough love--being firm and consistent in letting children suffer the natural (logical) consequences of their actions, while doing so in a very gentle and loving way, having true empathy in your heart. My mom parented this way, and I really appreciate my upbringing. I feel she was a very effective and loving parent who helped prepare us for the real world.
If classes aren't available near you, check out some Love and Logic materials at the local library for free or buy them at www.loveandlogic.com. Here are some I recommend: a seminar on DVD "Painless Parenting for the Preschool Years," the book "Parenting with Love and Logic." They also have some great CDs full of wonderful advice and real-life applications that you can listen to in the car while driving.