I think if you take the side off the cot instead of her waking and screaming for you, she'll get up and come into your room. Maybe that will be easier for you? Maybe being able to cuddle her while you lie on the floor in her room will help? But it won't actually resolve the problem.
This is behaviour issue and I would test it as such. It's unwelcome behaviour, she is behaving in a way you don't want her to. So for her own good you need to correct that behaviour, whether she likes it or not.
So I would stop reading until she's aslerp asleep at bedtime. And stop lying next to her in the night. Develop a mantra you say: "sleep time now, we lie down quietly at sleep time. Nan night" (or whatever) and repeat it every time.
Explain to her what will be happening. Give her plenty of forewarning and set clear expectations.
At bedtime read one story then into the cot fully awake. And let battle commence....
I'd go in and out of the room at times intervals. Repeat the mantra, don't expect to calm her down just repeat your expectations and leave. Over and over and over and over again.
Same in the middle of the night. Expect a tough week and a very tough 2 or 3 days initially. But be consistant.
Maybe she'll scream so much she's sick? It happens. Just clean it up, clean her up. And continue where you left off. Maybe she'll climb out the cot? Be cross with her - as you would with anything dangerous she might do. Tell her off. Then carry on as you were.