Asking this of DD's primary school? And how should I handle it...

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DD(10) has turned out to be quite musically talented. She isn't setting the world on fire or anything, but she started piano and singing lessons a couple of years ago and has flown through a few grades. She really enjoys it, works very hard at it and I think it teaches her some brilliant skills (practice makes perfect, hard work equals good results etc).
For her birthday, she asked if she could take up a string instrument which I have also encouraged as she then gets to be social with it, orchestras and such. She's been playing six months, doing well but obviously still learning the basics of technique.
She's just gone into year five, and the school has a session once a week that the year 5's learn a string instrument. Her cello teacher has explained that at this stage it would be a terrible idea for her to essentially have two teachers, so could she not take part for the time being.
I spoke to her teacher this morning, and explained the situation and was told as it is a whole year group session they have no where to send DD, and why do I not want her taking part? I explained (again) I was paying for private tuition and that at this stage it would be very confusing for her. I did say I was happy for her to join in maybe in another six months, and she was more than welcome to send home pieces for DD to practice. The teacher has said she will have to speak to the music coordinator. The teacher was abrupt and rude, and fwiw I kept smiling, explained myself calmly and politely and left with an "ok, let's see what we can come up with".
Tbh, I'm struggling to understand how they can even teach 60 kids a string instrument all at once, in one hour, but that's their logistical nightmare, not mine. I don't want to fall out with the teacher (DD loves her), or the school, I will have three DC's there at some points, but I really really don't want them, for want of a better phrase, to cock up something I'm paying for to enrich DD's life.
AIBU to ask them to excuse her from this? And how should I handle it from here?
Please be gentle, first AIBU!

Are they all learning cello or are some of the children doing other string instruments? If the latter, why not ask if your DD can play something other than cello in the sessions? maybe give her a violin instead? That way she won't be bored (as she will probably be more advanced than the rest at cello) or they could give her a go at the piano accompaniment? But yes, if it's a whole year group activity it will be a headache for the school to find separate supervision for the children who are having private lessons, and I can understand the class teacher thinking you are being precious, sorry.

Well, YANBU to think the school is being a bit ridiculous - a string instrument requires smaller groups than something like recorder if lessons are going to be effective. It's a waste of money.

However I doubt that any harm is going to come of it so I would just let your dd join in. You can remind her that if in doubt she should follow the advice of her real teacher. So YABU to kick up a big fuss about it.

She's 10, she can manage to sit through the lessons and keep a low profile.

Dd2's whole year learnt the ukulele last year yr 4). They actually sounded perfectly pleasant. the LEA music people put on a concert and a ukelele band made up of primary school pupils from the whole area played - must have been in the region of 80 children all playing at once. You've never heard The Lion Sleeps tonight or Sam Smith's Stay with Me played quite like it.

Your private teacher I worries she'll prefer the other teacher.

My dd2 was in exactly that position as your dd. Her teacher was delighted with the situation. The class teacher used her as demonstration and also she played a separate line to their accompaniment.
It was great for her and the private teacher supported it totally.

It won't cause any damage to sit through the wholly ineffective group lessons. Chillax.

I would understand if you were considering 2 different private tutors. Then it may be confusing.

However it's two different things and she shouldn't be expected to abstain from a whole class activity.

Dd is a kick boxer, her school runs an after school kick boxing class (so optional), I would be baffled if staff at the dojo she attends twice a week (and competes for) told her she couldn't do both.

Maths tutors don't tell parents to abstain from math classes do they?