DD can't sleep in boarding

If she's used to sleeping on her own, I can see why that would be a problem. My 2 youngest are in bunks, and when DD2's away, DS2 has trouble sleeping, even though he's asleep when she comes to bed.

If your dd moved rooms and her sleep reverts to normal. - job done. If the move proves that it’s nit the dormitory then it’s process of elimination , but it will also be another upheaval and unsettling.
Are there other process if eliminations that can be tried first

At DDs school they’ve already had a mini switch around in a couple of the dorms, and will almost certainly have another when the girls go back after Christmas.
I think if there was an unsettling incident in your DDs current dorm then a move might be all she needs to get settled.
Also you say your DD is in room with 11-13 year olds, would it be possible for her just to be with girls her own age/year group?

I would start with asking that she move dorms. Once it’s done, they may need to make no more interventions, so they will probably readily agree, if there’s a space. Is there someone she would like to share with?

From what you're saying is a trigger of some sort is within the room? or from domeone who is is the room? So you already know the problem ask for her to be moved rooms.

Hard and all as this seems to be for you to accept, you are the girls parent, it's up to you to make sure your dd has a safe, happy home environment.

I would suspect stress is the cause

She probably just needs you and the safe feeling that being in your own bed and home brings.

I suffer from insomnia like this from time to time, I have found taking a phenergan tablet in the evening makes me sleepy earlier in the evening and although I do still tend to wake in the small hours I fall back to sleep much more quickly. phenergan is an old safe anti histamine also marketed for travel sickness, nausea and insomnia, its cheap and available over the counter and can be used by children. I find it useful to break a cycle of insomnia ( usually caused by stress or a fright) and take it for two or three days ( it's not recommended for more than a week unless on prescription). I do need a large coffee to get me going the next morning though!

I also thought Fitbit to see for certain how much she is actually sleeping. V surprised school seem to be brushing this off. Sounds like it may well be anxiety or MH related, or it may be noises/triggers and a sensitive sleeper, or if happening at home too may just be too tempting to be up late chatting or on line etc and then can’t sleep (you mentioned if she had a device in the night she would be gaming). Only OP will be able to guess at the reasons - but I would have expected a boarding school with any decent type of pastoral care to want to get to the bottom of it

I would be wary of restricting sleep further. Generally sleep disorders involve letting her sleep when she’s tired.

I boarded. Much was made of how if you were any sort of a person you’d love it. Lots of my friends still say they loved it until after their 3rd glass of wine. Talk to her without preconceptions and tell her you won’t be disappointed in her if she hates it.

Can she swim in the evening? Or do some other physical activity. That will give her good endorphins and help her to feel tired at the right time.

I like wax earplugs best - I get them from Home Bargains.

What about a watch like a fit bit - that would give a good indication of her sleep routine.

There’s a good mindfulness app on the Apple watch. You could monitor heart rate then too which might give you some insight.

I can recommend Max-lite earplugs, you can get them on ebay.
They are the only ones that don't hurt my ears because they are so soft.

Thinking along same lines as Bertrand, was there a ghost sighting or something?

Was it a ouiji board or something like that?

This all sounds very unsavoury!
Your kid is very young and loves away, she can't sleep
She's living at a new school she doesn't know and knows nobody there
There was an 'incident' which has had led to a relatively long term upsetting reaction
She's sleeping in lessons
The school isn't responding
You're not stepping in
Your child is suffering

I'd be in the car by now

On one side they deny their is a problem because they are not aware of evidence of it, on the other teachers confirm that there is sleepiness in lessons
So your dd saying she is having sleeping problems is not enough for them, they want evidence?

How many girls are in the dorm and what age ?

Work on the causes of the triggers and the creepy experience, it may be that when she feels triggered by her experience she is taught to stroke her teddy or to visualise a calm and happy place, meditate etc.

You may need some professional help if you want to see a solution sooner rather than later, I would not advise leaving this just to resolve though, chances are it will continue to play out.

If you can do this with her during the holidays, and resolve it at home she may manage much better at school.

Keep supporting and listening to her.