Vete a hacer pucheros

[poli]

I think it means go jump in the lake, or get out of my hair but I'm not too
sure. Can someone confirm this? Thank you.

[chileno]

I think it means go jump in the lake, or get out of my hair but I'm not too
sure. Can someone confirm this? Thank you.

Yes, it is to get out of your hair, or let me alone.

In Chile, when a baby/child is crying and doesn't get consoled for whatever reason, more often than not, we say "anda a llorarle a tu abuela"

[hermit]

I'm not familiar with the phrase - but might there be an additional
connotation as well, like "go somewhere and sulk"? when a child pouts,
for example, se dice que "el nino hace pucheros.".

hermit

[sosia]

I'm with hermit
"vete a hacer pucheros" means "go to pout in another place"
Example
"Si no te gusta mi decisión, te vas a hacer pucheros a otra parte, no la pienso cambiar"
Saludos :D

[ROBINDESBOIS]

Hacer pucheros en mi pueblo es enfurruñarse. = to pout