I think @Starwarsepisode3’s advice is good, @RunningThroughMyHead.
I used to be an operating theatre nurse - I did 8 weeks in the theatres at the Eye Hospital in Manchester, as part of my post basic theatre course, but don’t have a lot of specific experience of eye surgery, so what I am saying is more general.
As people have said, the surgeon who is learning this procedure, under the consultant’s supervision, will be a fully qualified doctor with experience in surgery - maybe years worth - following qualification, before they specialise - in this case, in ophthalmic surgery. They will be experienced and skilled in surgery, and will have done less complicated procedures, first supervised and eventually unsupervised. Basically they will have started with the easiest procedures, and worked their way up to more complex ones.
But you have every right to feel anxious about this - having a child undergo surgery is pretty scary, as I know from experience - and the letter clearly added to that anxiety.
As I say, I think the advice I’ve quoted above is good - you may feel better if you have more details, and answers to the things that are worrying you. There is evidence that shows that patients who have all the information they need, prior to surgery, show fewer markers of anxiety post op, recover more quickly, and lead less pain relief - and it makes sense to think that the more information you, as the mum, have, the less anxiety/stress you will have.
A good consultant will be happy to make sure you have the answers you need, and should try to set your mind at rest.
Finally, although it is a while since I worked, it is my understanding that the patient (or if the patient is under age, or cannot make the decision, their next of kin) can refuse to have a student perform a procedure on them, and I would assume this applies to trainees too. Since the consultant will have to be there, to supervise the trainee, requesting that the trainee does not perform all or part of the procedure won’t change the staffing in the theatre so I can’t see any practical reason why they should refuse that request, of the consultant can’t set your mind at ease.