If my school aged child needed a diaper change at the beach I would change their diaper at the beach.
I would cover them up the best I could and then lay them out on a towel and change their diaper or if possible I would take them to the vehicle to change their diaper.
But if I could hide their private parts etc I would change the diaper right then and there if needed.
I've seen a kid of around 6 years old get his diaper changed on the beach by his mom last summer.
He was also just wearing his diaper and shirt and ran around the beach wearing just the diaper and shirt and was playing in the sand and making sand castles.
I also saw another older kid of around 8 years old at the beach the same day who was wearing just a diaper and shirt and sandals.
He was playing in the sand pushing toy trucks around like that.
He also got his diaper changed on the beach and his mom laid him down on a towel and changed him right there and he didn't seem to mind.