I ignore a lot of stuff. Children over 4 who tantrum in the supermarket get a lecture about acting their age and a reminder that I will only listen to them if they make reasonable requests in a reasonable voice.
I never buy things snuck in the trolley - I send the child to return it to the shelf if I discover it at the checkout (or before).
I say no a lot.
I mostly ignore them and get on with my shopping.
I take a list and stick to it if it's getting out of hand with overpsending.
I do fortnightly shops to reduce their frequency.
I use bakeries, butchers and fruit and veg shops to reduce the time in the supermarket with the overpriced sugary crap in.
I remember that the school holidays don't last forever and when school goes back it will settle down again because I can go while they are at school