If it wasn't for DD2, I would have long periods where I thought I was an absolutely hopeless parent because DD1 is just so challenging in many of the ways that you've described.

My friend and I used to say, "if they will sit in time out, they're not that naughty in the first place."

It sounds like you've tried virtually everything and I think that seeking professional advice is a good idea. In the meantime, what helps me with DD1 is to spend lots of one-on-one time with her. This can get tricky as DP is not here in the evenings and DD2 goes to bed very late. Nevertheless, we had "special movie night" the other night which after DD2 went to bed didn't start till 9pm and because it involved a bath with mum, blowdrying hair before the movie even started ... didn't finish till midnight. But you do what you have to do.

If you find the answer, tell me because DD1 can be a real handful at times. DD2, on the other hand, with much slacker parenting is an angel (apart from bedtime).