OP, from what you say about her writing and based on the fact that she appears to be about to go into Y3, it sounds like she is struggling quite badly with literacy.
I do find myself asking what on earth this school has been doing with her for the past 2-3 years...?
For a start, is the school teaching systematic synthetic phonics correctly and consistently? This is the approach which all British schools using the NC are now expected to be doing. Is there an element of...they are kind of wafting through using a muddle of different methods? If all the school's kids come from privileged backgrounds, perhaps the school has got used to the idea that they can just rely on parents and tutors to sort kids out at home.
Also, why is the school "laughing off" her difficulties? That sounds quite shocking to me. They should be taking difficulties seriously, and they should be assessing her and sorting out problems well before Y3! Why is Y3 the earliest that they will take her concerns seriously? That sounds like a load of rubbish. Has the school not carried out the Y2 phonics screening? If they had, then her difficulties would have stuck out a mile and the school would have been forced to take some action.
You say that the earliest you would be switching schools would be Y4. But from what you have said, it sounds like she is far behind with literacy and the school sounds extremely unhelpful and probably not capable of providing any useful remedial work. Surely she is just going to end up wasting another year drifting through in a classroom where she cannot possibly do the work and is also not accessing the remedial help she needs to catch up?
Frankly, I would pull her right now and get her a program of one-on-one tuition with a teacher who will teach her synthetic phonics properly and get her sorted out. You may well find that her apparent "learning difficulties" disappear when she has had some proper individual help with someone who actually teaches her to read.
The outdoor activities and seaside fun etc. at Beeston Hall sound lovely and all, but your daughter needs to learn how to read and write properly, otherwise it is going to affect her life chances. Does BH actually provide proper phonics intervention for children who struggle with literacy and do they actually have a track record of turning reading problems around? If not, then they will be a waste of your money, just like this current prep school appears to be (sorry to sound a bit harsh, but that is the impression I am getting).