First, if possible, I think that the natural parent should attempt to fill the role of the disciplinarian; the stepparent should be supportive and not try to take over this role. Children are bound to be resentful at some level of "the new husband," especially at the beginning. Add to this resentment of the stepparent for ordering them around and punishing them, and you've got a major family problem that can easily escalate into an ongoing war.
I think that as hard as this sounds to you, you should not take their behavior personally. If you can enter into a co-disciplinarian role with your wife, you should never discipline the kids without your wife's cooperation and approval. Don't take charge of these kids and don't have disagreements over the kids in front of them.
Two good resources to begin your learning with are: The Parent's Handbook by Don Dinkmeyer and Gary D. McKay and Discipline Without Shouting or Spanking by Jerry Wyckoff and Barbara C. Unell.
Good luck. I know you might be at your wits' end but you clearly want to do best by these kids. I applaud you for your efforts.