Also worth noting that California appears to have a notification system for spraying certain things. It needs to be notified and recorded. So if worried, it would be worth checking what the UK regs are on it.
And when it comes to statistically significant or insignificant, the boffins are pretty good at spotting the difference, even though childhood leukemia is rare in the UK. About 650 cases per year, if there was a cause they would find it. That is what these studies are about after all.
If a significant % of these 650 cases per year were linked to garden centers, we would know about it.
So I think the OP can put their mind at rest. Maybe talk to the facilities as you say. Ask if they spray, and what they spray, and if they are spraying, then ask for a bit of notice to shut windows. Depending on the wind. I doubt they would spray in high wind anyway.
I remember decades ago in Scotland there was an incinerator that caused worry of baby deformities. The incinerator did handle dangerous stuff. I can't remember the details but it was shut down. Here is a link to that.
Re-Chem International Ltd - Falkirk Council
I post that, because the UK does take these things seriously.