I have tried the more hardcore method, leaving the room but she became hysterical very quickly, cried, vomited and on the last occasion she shook. She was on her own for approx 2 mins but she was that afraid she was actually trembling.
You need some perspective.
She will happily be in the lounge while you are in the kitchen, she can be at the childminders while you are not even there. I assume she will potter off at playgroup etc without clinging to you?
I put to you that the screaming until vomiting and trembling is total blind fury. She is angry. Very angy, furious at you for expecting something from her that she doesn't understand.
Just because she doesn't understand it fully doesn't mean it's wrong. You are the parent and adult. You do know what is best.
Realistically, at the point you are, you can make some small changes to gradually progress towards independant sleep. But it's going to be very slow - I'm talking a year or two.
Or just bite the bullet, stand your ground on the basis that independant sleep is better for her whether she likes it or not. And deal with the fury.
The Gentle Route.
This isn't going to mean own room now. Get the cot into your bedroom. Initially take one side off tge cot and wedge it up to your bed. Its an extended space off your bed then. See if you can encourage her and bribe her into it every now and again. Work on establishing her sleeping in the cot consistantly, with the whole of the top half of your bidy in the cot too, cuddling up.
This might take several months. Then extract yourself so she'll settling in the sidecar cot with just your arm around her, not cuddled up. Then work on removing that arm so she sleeps independantly, but right next to you.
Then side on the cot, but next to your bed. Arm in the cot reassuring her as she goes to sleep. Then a foot or so away ftom the bed, but still settling with your arm/hand in cot if needed. Then the other side of the room. Then..... Then then try in her own room with you teaching into the cot as she goes to sleep.
The Bite-The-Bullet Route
She's going to scream
She's going to be angry
Shes going to be utterly furious with you
Make attempts to explain what will be happening at bedtime, you may be surprised how much she understands.
At bedtime make sure she has all she needs - has had a drink, isn't hungry, has a comforter.
Follow your routine, put her in the cot standing up. Don't aim to lie her down, she can do that herself at this age. Say nan night and leave and close the door.
She'll scream. Wait for 5 mins. Go back in, don't pick up, give her an in-cot cuddle (standing up), extract yourself, say nan night, leave, close doir. Wait 5 minutes, repeat....
She may well vomit. It's quite likely - it happens a lot when children scream. No big fuss. Go in, clean up, chsnge clothes if needed, continue. The vomiting is mo reason to stop. It's a simple physical reaction to screaming, not an indication of her well being.
She might tremble. She will be furious. Just because she's (very, very) angry does not mean she knows her needs better than you do.
You just need to be sure of yourself if you do this. That's all. It will be horrendous for 3 days or so, but she will quickly accept that sleeping is going to happen in the cot no matter what she does.
Once consistantly keeping her in the cot regardless of what happens, and the battle to accept the cot as the place for sleep is over, then you can start being as gentle as you like with her. But you will need tat battle initially.