"Dezelfde, diezelfde, beide" take -n in plural when they refer to people:
Het zijn altijd diezelfden, die geld verdenen. - It is always the same (people) who earn the money.
I just had a sentence "beide kinderen ziet niks" so this way of seeing things doesn't seem right
He means that if the real noun, as in your case "kinderen", then you use "beide". If you want to litteraly translate e.g. "both swim", you have to say "beideN zwemmen", as now "beiden" is the subject, and not something related to the word that makes the subject.