A lot of people disagree with me on this, but if I ever remarry, my kid had better treat my new wife with the same respect that she treats her own mother, because in my house, the adults rule. My new wife will be able to dish out the discipline, without any interference on my part, just as if she squeezed the kid out herself.
I will also expect the same authority over her kids, if she has any. There is no room for a castrated parent in any household.