waterproof coat for 13 year old DD

[parietal]

my DD (age 13) has a decent walk to school (20 mins) that has to happen regardless of the weather. So she needs a rain-proof coat of some form.

any suggestions for what she might actually wear within the rules of teenage fashion? she says no to everything i suggest. her preferred clothes are wide jeans and white trainers and a giant hoodie.

what shops should I take her to? budget up to £100 but £50 is better.

Can you treat something non- waterproof with Nikwax?

I don't think I can treat her hoodie and she doesn't want to wear much else.

what shop could I take her to? she doesn't even really know what she wants.

What I did was provide the plainest black waterproof I could find with absolutely nothing on it at all, decent shoes and an umbrella and then left her to it. If she got wet then she was wet.

H&M have this

www2.hm.com/en_gb/productpage.1215362002.html

North Face.

My younger son flatly refused to wear any type of 'raincoat' on his walk to school. He would take a mans umbrella if it was hammering it down. He barely wore a coat in the winter, just the standard hoody over his uniform. I gave up in the end and left him to it. He's now a sensible 20 something who has a huge collection of coats for all weathers. As a teen myself, my Mum bought me a duffle coat from the school outfitters in green, which I absolutely hated. I was teased relentlessly about it and will never forget the humiliation of being 'sensible' instead of trendy! 😂

All of the teens near us where a black puffer style jacket, preferably cropped. I'm not sure how this will work in the summer but I've been pleased that this is the look as it means they're actually wearing a coat rather than just a hoodie.
DD's is from Pull & Bear.