I say whatever helps your child go to sleep. We as parents and the crazy daily routines we have, we do not want to fight our toddlers with bedtime, we also need sleep! So if the tv helps her sleep, then so be it! I fall asleep with the tv on everynight and i sleep fine. As long as your child is not staying up all night watching it, she should get plenty of sleep. I dont believe all the studies that these scientists or whoever do. But to make sure she is getting sleep, set a timer on the tv to shut off in a certain amount of time, for ex. set it to shut off in 30 minutes.
As for the shutting the door and making sure it has a child-proof door handle cover on the other side so your child cant open the door. Well out of curiousity, does this mean you just ignore your child who is in there screaming cause they have the feeling they are locked in? I dont know, but i think that is very mean! If you really listen to nanny shows or read articles in the parents magazine, they tell you that you just have to explain bedtime routine to your child and make sure you stick to the same routine every night. If they get out of bed, you get up and put them back in until they fall asleep. If this lasts an hour then so be it. Well good luck, i am battling sleep time myself since my 2 yr old decided his bedtime was no longer 9pm, it is now in between 10-11pm.