Would it be incorrect to not include 儿 here? For example, what's the difference between 那边儿 and 那边? When writing in Chinese do I need the 儿 because I've heard people say both.
儿 is Pekingese (beijing dialect), like "lah" in singlish (singapore english).

https://en.wikipedia.org/wiki/Beijing_dialect

https://en.wikipedia.org/wiki/Singlish#Lah

in general, you don't need to write it; unless you want to impress readers that it's pekingese.