To believe my DD when she says she doesn't vape

I think it is highly unlikely that the teacher is lying.
Your daughter has already broken school rules, by using her phone, so she is not scared of school sanctions.
Don’t be naive because your daughter could be hiding something here. If she can’t afford vapes, but was spotted with one, is she selling them?
This is not unusual behaviour for a teenager, but make sure she understands what the school is saying. If suspension is the consequence of vaping again, then remind her.

Exactly. It doesn't break her trust if you say that you are testing so you can tell the teacher she has made a mistake.
OP, you can say: " I believe you, but I want to do this test so I can tell Miss X that it must have been someone else. I completely respect you have a lot of kids lying about vaping, and she looks very like other girls in the year, so although I trust my daughter, I did this test so I can confirm to you that she is definitely honest".

The teacher wouldn’t lie… she’s vaping! Ffs! We all lied at that age shout smoking/drinking etc… I’d be furious

If there was a second allegation - one with actual consequences rather than just a warning - she might then be willing to be tested to keep her name clear.

I think I’d give her the benefit of the doubt this time. I did barefaced lie to my mum about smoking when I was her age as did most my friends. When she found out she stopped my pocket money for AGES because she said I’d lost her trust and it would take a long time to gain it back again.

If she were my dd, I’d hope she was was telling the truth, but be prepared with a well thought out consequence in the event it proved she wasn’t.

Of course she's bloody vaping

With no real proof there isnt a lot you can do but accept her explanation. Advise her not to hang around in a big group and that if she is caught she wont be going to prom.

You’ve asked her, she’s given you her answer.

You don’t want to keep questioning her as if you don’t believe her because it will make her lose trust in you and not want to tell you things.

Just remind her what an awful habit vaping is and that you believe she isn’t doing it and it should stay that way.

Tell her that you hope very much that she would not be stupid enough to vape, and that this is a case of mistaken identity, but that you need to be sure. You can then tell the school you have tested her, it was negative, and so it must be a different pupil who was seen.

She probably vapes

I know parents who buy it for their kids who then sell them at ... School

Yep.... Shops will not sell them where I live but some parents but extra...

So maybe think how does she get the money.. there could be other things going on.

A teacher saw her?

So why would the teacher make this up

You dont have to be your kids friend you know. Talking of 'losing her trust'. She has surely lost your trust by vaping and lying?

Why would a teacher make this up?

cross post, but i think thats about all you can do at this point.

I’d have said the same at her age about smoking and i’d have been lying through my teeth. not that that means she is lying, but it also doesn’t mean she’s telling the truth. I’d just let it go, tell her that what you believe at this point is immaterial, what matters is going forward she needs to be nowhere near anyone vaping.

If she is usually trust worthy I would believe her, especially as there is no proof she has. My dd was accused of vaping and it being seen in her pocket, I knew it wasn’t true because how she feels about it. When I asked her she laughed and showed me her mascara which was in her pocket and looked like a vape from a distance.

I would be telling the school you do not belive it was your DD vaping, you will not accept any school sanctions without proof, a teachers word against your DDs is no different to another pupils without proof. They could quite easily got your dd mixed up especially if she was seen from a distance.

I mean you could buy some nicotine tests and see if she’s willing to do one?

I’d accept that I didn’t have enough information to tell whether she was telling the truth.

Unfortunately, every single one of her statements would be said by any kid I've watched get a fresh Elf bar refill box out of their bag, unwrap the new cartridge, take the silicon bits off, insert into the vape and stand there chatting, vaping, selling extra ones also in their bag to Year 7s and 8s, whilst I watched them out of my window.

And, equally unfortunately, at least half of them would have parents that absolutely believed them saying 'It wasn't me, I'd never do that, I've never vaped in my life, search my bag, I'll take a lie detector test, it's mistaken identity, the teacher's got it in for me, I was there and some other kids were doing it, I don't know who they were, I've only been at school with them for five years, it's not fair' and probably a few tears of woeful disappointment as to how the wicked teacher could ever think such a terrible thing of them.

I would probably stay on the fence, reiterate that vaping is bad for the health of people who do it. It sounds like the consequence of doing it again around school is hopefully enough to put her off doing it again if she did. Just keep an eye out/maybe go through her bag another time in a few weeks when she wouldn’t have had chance to get rid of one.