No one here really knows the details and extent of the problems in Winnipeg, and even if someone knew, they wouldn't tell us on a public forum. What we do know is that trading Laine seemed to fix nothing. But honestly that doesn't tell us all that much about Laine and whether he was a "problem" or not, all it really tells us there were problems that had nothing to do with Laine.
Laine never publicly demanded a trade from Winnipeg, it was when it seemed they couldn't agree on an extension that his agent hinted at it publicly (edit: as in, "maybe it would be best"), I don't know what happened behind closed doors but he never "quit" on that team. He had a decent 19-20 season where he showed no signs of "quitting" on the team and his only game in 20-21 as a Jet he was everywhere, putting up the numbers and throwing his body around until he got injured. Compare that to players who actually quit on their teams, "the shift" and things like that. I get it some fans are salty just from a player wanting out, but there's a big difference between being a pro about it (which Laine was) and "quitting".
As to the situation with CBJ, keep in mind no one knew about the trade request until the CBJ management revealed it months and months after the fact. So he didn't demand anything in public, there was not even a hint at it.
Wanting out of two teams in a row is not a great look, but it is what it is, hyperboling it with quitting and making stuff up ("publicly demands out") is just dishonest.