Fig.: to talk about private or embarrassing matters in public

Stop it! Don't wash your dirty linen in public! Let's go home and deal with it

Smettila! Andiamo a casa e parliamone. Ricorda che i panni sporchi si lavano in famiglia

Our neighbors are always fighting, even in front of others! They don't care about washing their dirty laundry in public

I nostri vicini non si fanno nessuno scrupolo nel litigare pesantemete davanti a tutti e così finiscono per lavare i loro panni sporchi in pubblico

Probably the reworked version of a French proverb "l faut laver son linge salle en famille" (You should wash your dirty laundry at home)