You absolutely have it right when you say she is exercising her authority. The problem is, a 3 year old doesn't have any authority to exercise! You and your husband set the rules. So what I would do is put her dinner out. If, after a certain amount of time, she doesn't eat, the food gets put away and dinner is over. You are right not to let her do anything else until the others are done eating. If she is hungry a reasonable amount of time later (say 30 minutes), then she goes back to the table WITH THE SAME FOOD. No eggs, no something new. Period. If she just pushes it around, she's done in 2 minutes. After the 2nd try, she is done for the evening. If she goes to bed hungry, so what? She'll make up for it in the next day or so, for sure. The next morning, you can even give her last night's dinner if you want to. "We don't waste food in our house" you know? She doesn't choose the food either. If you want to give her a choice of 2 things, fine. But that's it. You are not a short order cook working for a fussy customer - you are the mom.
You have to stop feeding her at 9 PM even if it's something you didn't cook. Your husband is right about that, but I think he's wrong to sleep on the couch with her. This is just enabling her behavior and rewarding her for being stubborn. And I agree with you - I don't think she's getting enough sleep - it kind of shows in her behavior!
I would nip this Santa thing in the bud. Santa also doesn't bring things to naughty children who are rude to their parents. Neither does Cupid on Valentine's Day or the Easter Bunny.
At 9 PM, she goes to bed and turns off the light. She can scream if she wants to, but she does not get to sleep on the couch and watch TV. Put a childproof doorknob cover on the inside of her door so she cannot get out. Explain that it is time for sleep and no amount of screaming will change that. Then stick to it. If she tends to have tantrums, I would remove anything precious from her room just in case. Put a white noise machine in your room if you have to so that you can sleep. I hope you are absolutely kidding about getting her a TV for her room - this will be a problem now and an absolute nightmare going forward. What's next? DVD player and XBox and Wii? I know it's frustrating for you, and it does seem like a TV will solve things - and it will in the very short run. But you will just embolden her for future demands. Then what happens with your little one? What will she learn from this? In fact, instead of adding things to her room, you can start taking them away. With my son, we left his favorite stuffed animals and his special blanket (security items) and books, but all the toys (luxuries) went into the attic. It only took 2 days to get the behavior right. As soon as he straightened out, the toys came back. When he refused to wear a helmet while riding his bike, the bike got hung from the garage rafters - where he could see it - for a week until he figured out that bikes and helmets go together. Period.
Now, a very wise friend of mine told me that "You don't have to go to every fight you're invited to." So stop fighting with your child. Don't raise your voice, don't argue, don't explain until you are blue in the face. Just be firm, this is the rule, and try try try to ignore the screaming. Tell her you don't talk to screaming people, and walk away. It's going to be very hard to control your temper, but when she doesn't get a rise out of you and starts losing privileges, she'll learn very fast that she's not in charge.
You ask how to make it clear to her - just by doing it! Don't talk about it and then give her string cheese at 9 and TV until midnight. Everyone goes to bed, the lights go off, and that's it.
Good luck - find a plan you and your husband can agree on too. That's a very powerful message for a child - Mom and Dad are in charge together.