You have a lot of great advice on this board that makes a lot of sense!
I also have a 4yr old that referred to the TV as HER TV - When I heard her say that, I decided that she is watching way too much TV! :) So the TV goes off after a couple of shows in the morning and back on after dinner to watch a show or movie together as a family. TV should be a priviledge not an appliance like I was using it.
Get her more involved with responsibilities around the house - She can sweep the kitchen floor, help you fold laundry - match socks (even if she doesn't do the job perfectly, it's good practice, and she's doing stuff with you, more attention and bonding) Go for a walk around the block, collect leaves
She's old enough to follow simple directions, and be proud of herself for a job well done. This will build her self-esteem, too.
I let mine spend more time on her art and practicing letters, making cards for family members (no occasion necessary) so we can mail them. If I'm busy making dinner - then she gets to watch TV if she's had good behavior up until then. Same with the other kids - Get them "unplugged". If they want to play video games - they also need to earn it - How about setting up alotted time slots? So everyone understands taking turns.
I also have a 12 yr old. I noticed that the longer she spent playing Play Station, the more impatient and grouchy she became afterwards. She doesn't play violent games, I think it is the constant brain activity and not enough physical activity to match. They get overloaded with energy.
Yes, your husband needs to be your strong supporter. If he knows that the family will be more peaceful when the rules are followed, I'll bet he will be more helpful. (Mine's the same way - too soft)
Younger kids can get frustrated when they have a hard time expressing themselves with their limited vocabulary - Her emotions may be a lot for her to handle especially when she's got older siblings that can overpower her.