You 'sometimes' punish, but most of the time do nothing. And verbally correcting her obviously has no effect, so why do you keep expecting it to? The key to disciplining children is consistency. Which you yourself have shown you do not use towards your daughter. Right now your daughter knows that, most of the time, she gets away with whatever she wants. And *gasp, she does and says whatever she wants!
Not meaning this to be insulting, but it's a truth... you sound like you need to grow a pair. You let your wife dominate you. Now you let your daughter rule you. If you let your wife do that to you, is it any idea where your daughter learned it from? Your 9 year old daughter runs your life and all you can do is come on here and 'gosh i don't know what i'm doing wrong'. What you're doing wrong is letting a 9 year old run the house and run you. How about setting some Real rules? Some real boundaries? Some real punishments? Try being consistent. Try being firm. Try sitting down and communicating with your daughter, instead of sending her to strangers to do it for you. Not that i'm against therapy, but for kids, that's only part of the solution.
And if you have her seeing two, then either you need to have found out that she has been diagnosed, by both, with some sort of mental disorder. Otherwise you are not helping her, and may be damaging her. If she feels that she is so bad and wrong of a person that she needs two counselors, then she may simply continue acting in a way that she feels she is viewed. Very common for kids and adults to act in the way they think they are perceived.
If your daughter has actually been diagnosed with a mental disorder then you need to be talking to the counselors too. Learning all about the condition, what to expect and the best way to handle her and her behavior.
It's also been established that people with mental disorders in 'advanced' societies like the US have a lower recovery rate than people in poor countries that live in villages and don't have access to mental health professionals. The reason? In the US and similar countries people with mental disorders are set apart and viewed as a problem, and treated differently. In poorer countries people with mental disorders are expected to work, pitch in to the village and otherwise treated normally. Because their mental disorder does not cause them to be separated from the society, they don't feel as an outsider, and conform to the role expected of them. This is healing. Those who are so bad they are not capable of living up to those standards are viewed as shaman. This is most common in schizoprenics, but i think there's an overall lesson about how we treat people and how it affects them.
If your daughter does well in school, but only acts like this at home, that pretty much proves it's not a mental condition though. It's not borderline anything. It just means she knows how she can act at school, and how she can act at home. Since most kids will push to get away with as much as possible, that's what she's doing.
I don't know the details of your married life, but she obviously has some bitterness towards you about it. Perhaps sit and talk with her about it. Or ask to go into one of the counseling sessions and plan out to have the counselor help this discussion.
It's time to take the reins back from your 9 year old daughter, stand up, be a man and a father and a leader. This isn't to say be dominating and controlling, it simply means to be in charge, and leave no doubt. It means to communicate. To take action. To DO something about your situation, not watch it happen to you. To quit making excuses for your daughter and learn the difference between being understanding and giving a little grace to a special situation (her mother dying) and being an enabler. It's not about breaking anyones spirit, it's about being a parent. Discipline is about teaching children right and wrong and learning consequences. Doesn't mean you have to break their spirit in order to do that. You're damaging her now. Discipline done properly would put an end to the damage you're causing her by letting her run wild, which you are basically doing. If you don't teach her now, in love, then someone who doesn't love her will put her in her place one day. And that will be way more damaging.
Love isn't passive, it's active. Sometimes it's gentle, but sometimes it's tough.