I'm quite sensitive to smells and hate the smell of stuff like Lynx and it makes me feel sick. The stink of a kid spraying it around in your home would be lots stronger than someone wearing it in work or on a train - it's 30 years on, but I still remember the.stink in the bathroom after my then teenage brother had a shower, with aftershave and deodorant and body spray, the smell was gagging.
It's your home, you're allowed to have rules. I've never had to face awful bodyspray smells at home - just realised I've been really lucky, as I would have done what you've done and told tweens/teens to bin them.
I have a no smoking rule in mine place as I don't like the smell - visitors get to stand outside if they want to smoke so I don't have to smell it for days.
I can't believe that 96% think you're being unreasonable - body sprays are not essential for hygiene, get her a decent deodorant- Mitchum is good - and some soap or shower gel.
Also, you told her not to get a spray, gave her the reason why, she agreed, but she went ahead and got them and then lied about it. Giving in, so she can be like her friends, would be a really bad precedent.