The problem isn't the bed. It's not the bedtime. It's the fact that you have both consistently stayed with her until she finishes playtime and is exhausted. She has never learned to put herself to sleep at 9 PM, and so she can't do it at 2 AM either. You are like the human pinky, the human breast, the human stuffed animal.
Aside from the fact that you are understandably going nuts, your child is not sleeping enough at one stretch for good brain development. So you have to get serious here. It's not just an irritation.
I'd honestly suggest the you look up the Ferber method. It's 3 nights of pure hell, and then it's done. No lying down with her, no waiting till she falls asleep, no rocking/singing to sleep, no snuggling. There's a set routine with bath, teeth, story (with cuddling if you want), lullaby, and a definite departure time. You don't go back in for a full 15 minutes. When you do, it's very little interaction - a few soothing words, "you can do this, night night" and a minor back rub or pat on the tushy, but no staying until she falls asleep. Then you leave, this time for 30 minutes. If you go back in, same routine, word for word. And so on. You do not reward her for screaming, you do not pick her up, nothing.
It's way easier to do this when she's in the crib because she can't get out of bed. She doesn't hate the crib. She hates not lying with you or Daddy. And that is no way to go through life.
And yes, I know you have 2 others who need to go to sleep. SO send them to Grandma's or to a friend's house on a long weekend if you have to, and go through this ritual.
It took us 3 nights, and it was awful, but then it was DONE. We did this on the pediatrician's advice, by the way - based on the fact that our kid was past 6 months of age and not sleeping all night.
Read the book, have your husband read it, and absolutely be in sync with each other on what you are going to say/do. If you deviate, it doesn't work.
Good luck. Fill your brain with the philosophy that you are doing this FOR her, not TO her. It's vital.