You're right-- this isn't a parenting forum, so I could see how it might seem "off-topic" or out of bounds to discuss parenting. And at the same time, I can't help thinking that our relationships with our kids (and our spouse's relationships with our kids) play a significant role in some of our marriages... so working on our relationships with our kids--and our parenting strategies--could, in a way, support our DBing!
My D3 can be fairly strong-willed, too. She generally behaves really well for teachers, her babysitter, her grandma... but lets it loose when I'm around. My friends have all told me that it's because she feels so safe around me. So, that's another way to look at it! Your D knows that you love her unconditionally, no matter how awful she behaves. And that's a good thing.