What should be done when kids get stubburn?

I guess some of it depends on the age. I have three children and the most stubborn out of the three was my daughter. When she got on a crying jag, there was no way you were going to shut her up. There were times I wanted to just pinch her little head off. What I finally learned to do with her was ask her, 'Are you mad?' she'd nod her little head yes, then I'd ask 'Are you going to stop crying?' and of course she would nod her head no. So I just took her little hand, led her into her room and told her it was okay to be mad, and she could cry all she wanted too, but she had to do it in her room. I would tell her when she got done she could come out. Within a few minutes she would come out and everything would be okay. What are these twins doing that is stubborn?