You have my sympathy. Your daughter sounds like more than a handful. To answer your question, your daughter is difficult. She might even be defiant, disrespectful, manipulative and a bully.
But she is six years old. You are the adult. Children test their parents. It's up to the parents to decide that they aren't going to fall for that manipulative behavior.
I'm a physician. I made an iffy call on one of my best friends in the ER (it's a long story). Two days later she presented in congestive heart failure from the massive MI she vehemantly wouldn't let me test her for (and I therefore missed.) I cried about it (mostly alone) for weeks. She became what we call a cardiac cripple (a terrible fate of some MI sufferers.) My eldest was a sponge and accustomed to medical talk. One time months later I was rebuking him for something he felt defensive about.
"It's not like I killed my best friend," he said. I looked at him with a mixture of awe and a bit of sorrow. "You're trying to hurt me," I simply said. "it was a good try." I didn't rebuke him. He was pushing. It happens. How often depends in part on how successful it is.
I can't address your daughter's behavior (hopefully others will.) But I believe you may feel things more deeply than is good for both (or all) of you. I would suggest you start in therapy to see why a six-year-old has so much power over you.
When you've explored this with a good therapist (it might mean you "shop around"), I think you'll be better able to understand her behavior, take it for what it is, and set reasonable limits on it consistently that might be more effective in bringing about a desired change. If she can't elicit strong reactions (spoken or unspoken) from you, her tactics will change.
In the meantime, I would recommend a book called 1-2-3-Magic. No arguing, no pleading, no bargaining, just a reward system for self control and time outs for lack if it.
(I also find the idea of a therapist ignoring your concerns strange. Most trust the parent.)