It doesn't SOUND like your husband has done anything inappropriate to her, but of course that's always one of the first things anyone would think after reading this.
Assuming, of course, that that isn't the case at all, another theory is that very often, kids choose to act out most with the ones they trust the most. My son is 2 and he will be a perfect angel with my mom, with my boyfriend, with almost anyone else he's with. Then the second he comes home to me he has an ATTITUDE, screaming and rebelling against ANY request, even if it's something he wants! That's just how kids develop comfort in a particular area.
I think your daughter feels completely secure in yours and his love for her, especially his, so she feels like she has a safe place to test boundaries without fearing the consequences, like she would with a stranger, or just someone outside of your immediate family.
This phase can continue for quite a while, until she gets a little older and learns that she can rebel in other ways (believe me, this is the easy phase! Next it'll be insisting she get a cell phone like every other girl in her class, putting racy pictures up on her Facebook, and throwing a fit because you wont let her have a boyfriend at age 11!)
My suggestion is to try the reverse psychology technique. Any time she needs to be told 'no', YOU tell her. Have her dad just walk away. Don't let him do any disciplining, don't let him have any say so. She is enjoying this game she's being allowed to play, so take away the other players. Force her to deal with only you, and since she hasn't been behaving badly to you, take advantage of that.
If she seems confused, great! She's no longer in control. If she misbehaves purposely in front of him, ask him to come tell you. You discipline her, and she'll freak out, wondering why her game is falling apart. Take the control away from her and you've won. I know it's annoying to have to play games like this but it will be worth it in the end.
She has to learn that YOU BOTH are her parents, therefore, until she turns 18, SHE HAS TO LISTEN TO YOU. BOTH. Right now it seems like although you've been trying to come down hard on her, you've obviously talked about how frustrated with the current situation IN FRONT OF HER, therefore giving her the satisfaction that she's 'winning'.
Also, you said "She also appears to become more and more withdrawn the more I bring up this topic". Which I'm taking to mean that you're just 'bringing this topic up." You're not sitting her down, talking to her in an adult way, explaining that it is not ok anymore. "You're a very big, smart girl. You're 8 years old! I should NOT have to have this issue with you, and from now on, it's going to stop. I will not ask you again to speak up, because you know it's what you're supposed to do. I expect you to do as you're told. End of story. Thank you." and leave it at that. Instead you may be pleading with her, or threatening. Either way, she's still in control!
The next time you want her to speak up, if she doesn't, COMPLETELY SHUT HER OUT OF THE CONVERSATION. Don't play the game! Immediately turn away from her and talk about something else. Don't mention your daughter or her lack of contribution- don't give her any attention for it. She'll be completely taken aback- "How did I just lose the spotlight?!" The behavior will stop. Immediately.
Also, by asking her grandparents to become involved you're subliminally telling her that you cannot control her alone, and that she's the boss. If you take matters into your own hands, and show her you're eliminating not only the other players but also her rules, she's got nothing. She will be so confused (and secretly glad to not have to be in charge) that she will give up, and swing right where she needs to be.
Of course, I cannot guarantee that but it worked for me and I feel like it's a pretty safe bet. Good luck!