Hi P.,
I used to stay in my daughters room when she was little. (she is now 4). That was a big mistake, and took some time to reverse. This is what I did.........
I realized that i needed a strict routine. (I'll try to make this as short as possible, but it's going to be hard) I stopped sitting in her room cold turkey, I picked 3 short books and stuck with them.(further down the line, I switched up the first two books but stayed with the same 3rd book) I also used the same key words to her as I left her room, and when she would scream for me to come back. I would walk in her room and say, "It's bedtime, sweet dreams, I love you." and walk out.......every time. (she never really got out of bed)
I think I read those same 3 books for a few weeks, until she understood that when that 3rd book was read, it was time to go to sleep. Of course, the whole process took about 3 weeks, but it worked. I was really hard listening to my daughter scream for me, but everyday got easier and easier and her crying spells got shorter and shorter, until one night I was putting her to bed, after her books, she simply said good night back to me and fell asleep......victory.
I know this is very different from your situation, and I do suggest consequences for their actions. But some type of consistency, and repetition just might work for them. I'm not sure that taking everything out of their room would work because they will just keep each other entertained.
You have to make this an easier process for your sanity.
If you have to keep putting them into bed (without talking to them) they will eventually get it. They are old enough to understand. Use a little tough love.
I really believe that because I was consistent, repetitious, and followed through, my daughter was able to know what to expect and do what she was supposed to do.
You might want to skip a video. My daughter is now 4 and her bedtime is at 7:30. (she usually falls asleep within 30 minutes)
Just stop sitting in their room. Tell them the rules are changing and they will follow the new rules or be punished. This is they way it is going to be or else. Plain and simple. I know, easier said then done, but it will be worth all hassle, I promise. The day my daughter went to bed with no problems, was a great night! We celebrated with a glass of wine and a little alone time.
Good luck to you and stay consistent!