We had this problem with our 6-year old (only) son. Like your child, he is extremely bright and verbal, and is also the type to run off in public places. Extremely confident and independent. But the hitting and biting used to mystify me; not so much any more.
I realized that although we didn't spank him, we provoked him regularly by reacting angrily to his "misbehavior" (I put that in quotes because sometimes it was actual misbehavior, but other times it was merely age-appropriate but annoying behavior, or we were asking something of him he couldn't comply with at his age, etc.). Being an independent and confident child, of course he'd "fight back" when mom or dad were acting like bullies. He was reacting angrily because we had taught him how! [And not only that, I've heard that a parent who reacts in anger seems to the child to be not-in-charge. And the child feels intense anxiety when the parent's being rattled. The child needs the parent to be in charge, to keep her safe when her own emotions are running high & feel scary.]
I've gone into this in other posts, but to sum it up, I was raised by an angry dad who was very strict; all misbehavior was met with anger and sometimes more. It never really dawned on me until recently that it wasn't the child's job to behave so as not to incur parents' anger.....it was OUR job to gently TEACH this newly-arrived-on-earth person who hadn't a clue and was looking to us for guidance as to what he SHOULD do. See the difference? So here he was being a normal little kid and we're expecting him (as most old-fashioned parenting methods would dictate) to just "obey." Fall into line, do as we say. We're the parents, that's why.
I have spent quite a bit of time observing other parents in our local group. Parents whose kids are sweet, gentle and happy. I wanted to know....how did they "get their kids to behave"? Well duh! Kids WANT to be taught how to behave. They want to make us happy and proud. But no kid feels happy and good about himself when he's constantly told: do this, stop that, go to time out, no treat for you....(i.e. endless stream of orders & punishments). It results in low self esteem and more anger, which makes proper behavior nearly impossible.
Ever since *I* have stopped bossing him around and have begun gentle/firmguidance style parenting, he has MOSTLY stopped lashing out. Not always. So, to make a long story short (too late for that!), I'd say, (and I don't know about your parenting; I'm basing advice on my own experience) try and look at what you might be doing to set her off. If she's very intelligent and intense, she's probably going to be very sensitive to what you do. Also, sensitive to what you'll put up with. My son occasionally tries to hit me when he gets very frustrated, and (as I explained in a different post about controlling temper), I just have learned to stay steady, deflect the blows, stay calm, don't react emotionally (and that means facial expression too; maintain calm eye contact)-- just be like a peaceful rock. Don't get her what she wants until she stops coming at you with her hands and ASKS for it. You want to teach her that she'll get the water, or whatever, when she asks you properly for it. I know it's painful; I have had my share of scary raised bite marks. But this too shall pass. :-)
I think that arbitrary punishments don't teach a child as much as this firm limit-setting does. You must show her what you will, and will not, put up with. I totally know what you mean about not wanting to take her out in certain places. I still struggle with it. But my son now knows that if he doesn't behave like a human being in the store or wherever, he will not get the special privileges that HE values, like going to the special play-place, the park, etc.
[And I say all this assuming that you've ruled out dietary reasons for the intense volatile behavior? I have heard other parents say that food colorings, chemical additives and sugar can make their kids act up. Just a thought.]
Best of luck. Oh, and to your DH I would say - No spanking. It just teaches your daughter that because you're bigger & more powerful, you get to win. And it's mean, in my opinion. I think it will just make her angry and harm the bond of love and trust between you (i.e. dad) and your daughter.
Yes, totally unsolicited advice, but from one who was spanked by Dad & feared him all my life. Thanks for listening & realize that (a) I really don't know your whole situation and (b) I'm pretty sleepy....busy day!! So no offense was intended in any of all that.
:-)