Hi charliecat, welcome to mumsnet! I did a quick search of the boards too - there is one in the sleep section called "Sleep and older children", which is mostly about 7-10 yr olds but might have some ideas for you!
I'm sorry to say it sounds like your dd has worked out exactly how to get all the attention she wants at night - as you say, if she doesn't then she will demand it the next day! I know it's tough, but you really have to be firm and consistent - if you give in just once (and I know it seems much easier in the middle of the night to just give in to keep the peace, esp when you have another child asleep!) then she will see it as a sign that if she persists long enough you will give in. If her screaming gets her what she wants, she has no reason to stop doing it. Buy ear plugs if you have to! But you need to stop being part of her game.
Maybe you could try some sort of reward system - if she stays in her bed, and is quiet in her room until morning, she will get a sticker/surprise/breakfast treat. Again, you have to be strict with this, if she doesn't do it, she doesn't get it!
What's her bedtime routine like? Does she go to bed without a fuss? Maybe have a timer, or a checklist, where she has to brush her teeth, get a drink, go to the toilet etc. If she has done it all in time, she gets a story/song etc. When she is in bed, say goodnight and leave - ignore any requests or complaints. Make sure she understands that if she doesn't stay quietly in her room, she won't get the sticker/reward. Calmly tell her if she calls out or cries, you won't answer her, even if she shouts. If she likes to sleep with her door open, tell her if she keeps calling out you will close it - and do so. Don't react to her, don't give her eye contact, don't answer her. Let her know you mean business - you can do it! She will get the message, even if it takes a week, it will be worth it. But it will only work if you DON'T GIVE IN to her calling out to you at all. Remember, you are not hurting or punishing her, you are doing her a favour by teaching her how to get to sleep and stay aleep by herself. You can extend the sticker system to the daytime too - reward for a tantrum free day! HTH and good luck!