Might you be remembering the short story "Final Solution" by Timothy Zahn? Looks like it was first published in 1982 in the Analog Science Fiction magazine, although I read it in Zahn's "Distant Friends and Others" book of short stories.
In the backstory of "Final Solution", the planet Kohinoor was founded by people who left Earth to escape warfare and conflict. But now it's on the brink of another civil war, when they encounter the alien Drymnu. As in the story you remember, the alien is very upset at discovering a space-faring fragmented (non-hive mind) species.
"Never before has a fragmented race survived its intraspecies warfare
to reach the stars. This has always been impossible."
However, in this story, the alien wants to just leave, but the humans (well, the main protagonist) ask Drymnu to help make them a hive mind, in hopes that will prevent conflicts (civil war, etc.). The Drymnu agrees, but problems ensue.
There's the child not able to play with a toy gun incident:
Ruhl Tras trudged outside to the empty field near his home, fingering
his ball restlessly. It was almost the only toy he could play with
these days that didn't bring a flood of disapproval from one part of
Kohinoor-mind or another. Some of his playthings were too dangerous,
to someone's way of thinking: others were considered a bad influence
-- especially his guns -- and others were simply deemed "childish" with an accompanying sense of guilt he couldn't understand.
There are also suicides (of war veterans who can't find any other way to stop giving everyone nightmares from their memories, for example), which is what makes everyone realize humans can't survive as a hive mind.
They end up building ships so everyone can go off and be alone again.
Small and cramped, they were little more than shuttles with sleeper
and recycling facilities, Burke star drives, and planet-scanning
equipment. But they would fly . . . and they would carry just one