i believe that one quinque that was "troublesome" was made from arata's, touka and ayato's father's kagune. and the one eyed owl (the coffee shop owner) said that the quinque is refusing to give his power to one of the ccg investigator. and the owner also said something about the soul of arata, so maybe he's still there with his children, meaning he never left them alone.
BUT!! what if arata is not their father's name but their mother's (i don't know whether arata is a name for male or female). Might be because on the ring it's written arata hikari. wasn't touka's surname something else? and how could they find their father's ring, when they don't even know where he died? maybe surnames work different in japanese or maybe the dad didn't wear the ring and left it at his home. Or they might've found out what happened to their father and where he died and so on.
anyways, i just checked their surnames and it is kirishama (touka & ayato). and at the start of the volume, it was written arata kirishama.. so it's confirmed that arata is their father, but what can hikari mean. Maybe it's a wedding ring with both of their (arata and his wife's) names written, like arata is him and hikari might be his wife? idk.