Kim Zolciak and Kroy Biermann painted the picture of a happy family during a low-key outing with their kids Monday ... a scene that drastically changed 2 hours later when cops were called to settle an explosive fight.

Both were seen together leaving a barbershop in Alpharetta, Georgia, with some of their kids in tow before making a stop at a nearby Starbucks.

On the surface, all seemed well -- but on closer inspection, Kim and Kroy were without their wedding rings again. As we first reported, not long after the errands all peace was shattered when one of their kids called the cops over their "extremely loud" argument.

Law enforcement sources told us 3 officers and a supervisor arrived at the estranged pair's mansion to try to settle the verbal domestic dispute ... eventually calming things down.

Officers are practically seasoned guests at the duo's home ... first arriving to the property in August when Kim accused Kroy of locking her out of their bedroom ... and a month later telling them she didn't feel safe in her own home.

October brought another revelation by TMZ ... with us breaking the story of a court mandate ordering them to keep their distance at home -- Kim gets the basement and nanny suite and Kroy gets the primary bedroom.