Hi There Page~
I wouldn't allow a TV in a kid's room. Unfortunately, you let that purchase happen. I know it was her money, but I'm pretty sure I would have told my daughter...feel free to purchase a TV, but know that it will not go in your room and then she could choose something else. Or if she came home with it I'd tell her the same thing and she could opt to take it back. Since it's already done and you allowed it to happen, maybe you could offer to pay her back for the TV and then sell it on Craig's List. Maybe tell her that too much TV is interfering with other important responsibilities and family time. It should be a privilege and as long as her chores are done, homework is completed and everyone is respectful of everyone else (no attitude) then she can have maybe 30-45 minutes of screen time (video game, TV, computer). I use an egg timer and when it dings, then the electronic gets shut down. If every week things go smoothly, then she can earn more screen time for the weekend, but not too much more.
Given you don't cave. It's important to set your rules and stick to them otherwise all of this is fruitless. And they've probably learned to whine because they know if they do it enough you'll give in. So, start all over. Tell them whining is an automatic "no" and then stick to what you said you were going to do. I tell the kids in my house... you don't have to like it, but that's how it is. I'm not in the business of making sure the kids like my every decision... in fact, if they did, then I'm probably doing something wrong.
Good luck! Stick to you guns!!!
A.