This is a great example of how counseling can be incredibly helpful. With someone for her to talk to, she can get some feedback on her feelings and behavior and learn more satisfying and productive ways to handle those "big" feelings. And you and your husband can learn effective strategies for helping her.
My middle son, who will be 13 soon, sounds a lot like your daughter. I have no doubt that if he can learn to control himself and channel his tremendous energy and personality, he'll be able to do anything in life - and it's my job to give him the tools to channel all the strength and energy and use it to move forward instead of just creating chaos all around him. He has been in counseling for 4 months and it has made a huge difference. For his dad (my ex) and I, it's great to have someone who really knows him and understands him so that when we get frustrated, he can a) validate that he really is difficult and that what works for a lot of other kids will backfire with him and b) give us ideas that will actually work.
For example, my son has had a penalty problem in hockey for all the years he has played. He's not old enough to hit but would check other players anyway and was in the penalty box multiple times a game, sometimes enough to be ejected from the game. So embarrassing and infuriating, because his penalties were stupid and selfish and put his team at a disadvantage. His coaches needed him though so they wouldn't bench him. We would ratchet up the punishment at home, keep him out of games, etc. and nothing worked. The counselor came up with a plan for him to "earn" his way into a tournament (which was an investment of time and money for us) with good behavior at home, completed school work, and clean play in hockey. That was enough to "flip a switch" in him and although the tournament was in early December, the problem playing hasn't come back. Now that he's playing clean, he's playing better - he gets more ice time, he makes better plays, he scores goals, and he's invited to play up with teams that are older or at a higher level. We created a situation where there was a big reward for doing the right thing, and natural, positive consequences have been enough to keep it going to a point where he's a completely different (and much better) player. His counselor has been working with him on understanding that his triggers - power and control - come from not being the loudest or biggest or toughest guy in the room, but by exercising the self-control to get what you want, often simply with words and behavior. That true influence is subtle and longer-lasting than bullying. That by changing his own behavior, he can change the behavior of those around him. These are lessons that he wouldn't have been able to learn from us.
I can't emphasize enough how valuable counseling can be in helping a very strong-willed child learn to manage herself. I totally understand the desire to keep escalating the consequences in an effort to "break" the stubbornness. I can tell you from experience that it doesn't work - they are younger, stronger and less distracted than we are and when they dig in, they can just wear us down. You might win some battles, but you're both losing the war. Really stubborn kids respond much better to positive discipline and the ability to earn things. Sometimes I get tired of having to forever have an incentive plan in place (this kid has to earn everything, including the right to wear an expensive pair of sneakers that he just bought with his own money) but his counselor assured me that over time - and it might be a very long time - he will internalize these incentives and manage on his own. In the meantime, we have a much better relationship, he's turned around his behavior at home, school and on the ice, and I don't feel like I'm banging my head against the wall every day or fear that I'm raising an incorrigible narcissist or someone with BPD.
I should add in that we had a complete neuro-psych evaluation done and in addition to confirming his academic aptitude and areas of weakness, it confirmed that he does have ADHD and he does take medication for that. The medication definitely helps as well as it increases his ability to make better choices and reduces his impulsiveness, but it sure as heck doesn't cure his stubbornness and grandiose sense of self, which is where counseling comes in.