Kelly Osbourne is apparently doing a whole lot better after her split from Sid Wilson ... with brother Jack Osbourne saying she's settled into a happier life focused on herself and her son.

Jack gave the update in a new interview with The Sun ... saying Kelly is "in a happier place" these days and has found a solid routine.

Jack says ... "Kelly's living her country life. She's just doing her thing, being a mom" ... adding she is now focusing on herself and 3-year-old Sidney, whom she shares with Sid.

As TMZ previously reported ... Kelly and Sid quietly called off their engagement earlier this year after years together, though sources told us at the time the door wasn't necessarily closed on a reconciliation.

Things appeared to get much frostier in August, when Kelly unloaded in a series of cryptic posts shortly after Sid was booted from Slipknot ... saying she was done protecting someone from themselves and asking for her dogs, belongings and "maybe some child support." She never named Sid in the posts.

Jack, however, isn't saying much about where Kelly and Sid currently stand.

Asked whether a scene featuring Sid should be cut from the family's upcoming documentary, Jack shut it down ... joking he'd get his ass kicked if he said the wrong thing.

Whatever's happening between the exes ... Jack says Kelly appears to be moving forward just fine.