To be honest, Jane in my book was completely justified. Kenny was unhinged and been so for some time, each time it seems he was coming out of it, he dips back into dark territory where he starts acting rash. She didn't do it to "prove a point" and she did say it went further than she thought it would. She did it to bring Clem to reality, you can't always risk an entire group and yourself for one guy. Not when that person is the very threat.
To be honest I blame, Mike and Bonnie more for Kenny becoming even more unstable. He was probably able to be pulled back out had it not been for that. That and the fact he (maybe Clem as well if you wanted Wellington), was the only one in the group wanting and arguing for going to Wellington. He is definitely no different from the selfish Kenny from S1, only out to protect what he deems as family. It gets many characters in S2 killed: Alvin (determ), Walter, and Luke.
I know it doesn't matter if you choose not to go to Wellington, but even if the group did make it there, it seems only Clem and the baby would of been able to enter. What would the rest of the group had done?
Kenny's hopes relied on blind hope (he does this constantly) and he was willing to risk everything and everyone (even Clem) to get there. He does "redeem" himself by choosing to leave Clem and AJ in Wellington, but that was the logical choice anyways and therefore I don't consider it redemption.
In the end, killing him is the easiest choice because it is the logical choice. The only reason for keeping him alive is due to the fact the players are more attached to him than any S2 character, due to TT's poor character development including bonding with the player throughout this season. S2's group was just some group Clem had to be with, unlike S1's group.
Another note: Why the hell did Luke not try throwing that AK, must of weighed like 8 pounds and his machete then tried moving faster? There was no point in standing still or moving slow once the ice started budging. Unfortunately, I think it is due to Bonnie/Clem trying to save him that finally breaks the ice. By trying to save him, they effectively killed him off in the process.
Also there was no reason not to go around the lake. Why risk your whole group crossing ice?