You are in a difficult spot and have my prayers for your wisdom in how to move on from here. It sounds like you are very tuned in to your daughter's emotional state and to some underlying causes. You are insightful! But that doesn't help...
Just to encourage you-- sleep is important for both of you, and it is good/okay/the right thing for you to do to insist that your daughter lie quietly with her eyes closed when it's time to sleep.
When I'm in a bind like this with my kids, I take time to figure out what my plan will be. You already have a bedtime routine--a great first step. Now process all these ideas you are going to get. You know how your daughter will respond to them. What will you do next? Have a plan, and write it down. Stick with it for a month, then see how it worked! Keep the goal of your plan clear... your daughter quietly lying in bed at a certain time, so you can do what you need to do to get rest yourself. You know your daughter best, so take what advise will work for you and her!
1.Routine-- you have that already. Does it need any changes?
2. Clear boundaries, whatever they may be for you, about how many "cover me up agains" they get (my kids just get one), "fill up water cups," etc. Eventually it has to end!
3. Emotional appeal-- "mommy needs to get work done so I can get rest too and be a good mommy tommorrow." The book, "Bedtime for Frances" is a great one for showing kids that their JOB is to go to bed!
4. I have given spankings to both my older kids (now age 4 and 5) when they were early 3 yrs for getting out of bed when they had been told they needed to stay in it or would get a spanking. It's hard, and I sometimes felt like a terrible Mommy. But bedtimes are now peaceful, and I'm so glad, especially since my oldest is in kindergarten. They just needed to learn where the limit was, and it didn't last. I hope my youngest can learn from his older siblings and not have to pave that path!
They are made to push limits and to see where the boundaries are. We parents are obligated to show them the boundary, with love, for the sake of the safety and well-being of our family. Mommy's sanity counts!
Blessings as you find your boundary-building methods...