The link you posted here gives legal definitions that I don't think that fully apply to Kenny's situation, tho. The legal definition of provocation (as you posted) in most countries work more or less like this: "conduct that would cause a reasonable person to lose self control". Let me give an example: let's say somebody put a lot of effort into writing a book (years and years of work). The book is almost finished, and I decide to set the book on fire. The person loses self-control and kills me. The legal definition of provocation would apply - this is a situation that could make a reasonable person lose self-control.

Now let's say I tell somebody, "baby, you are my sweet little banana". In the person's mind, this is a provocation, a terrible insult, which makes them have an anger outburst and kill me. You could say I technically instigated the situation, but the legal definition of provocation doesn't apply. This isn't something that would make a reasonable person lose self-control.

Now let's examine Kenny's situation. Jane told him the baby acidentally died, which is something that could easily happen at the place they were. Kenny doesn't even ask for specifics, and decides to kill her in the same minute. It is definitely debatable at best if this is a situation that would make a reasonable person lose control and murder somebody, especially given how the baby isn't his.

Note: Of course, I don't think Jane is right/guilt free, either. I think both Jane and Kenny are wrong, and that two wrongs don't make a right. Kenny's actions can't be justified using Jane's mistakes, and vice-versa.

Another thing is, all those definitions and laws work to protect people IRL, under normal circumstances. In real life, we seek to help someone who has problems with short-temper or anger, and give them psychological treatment. What do you do with someone who easily snaps/get into angry mode during a zombie apocalypse, though? You have two options, basically: you leave/kill them, or you accept to be around them, which will hinder your chances to survive.

How does Season 2 shows growth in Kenny? In Season 1, Kenny's character is heavily characterized by his lack of ability to be flexible with other people and compromise. He is also characterized by lack of rationality and his extreme loyalty towards people who are "his" (his family and some few close friends) and his aversion/aggression towards new people or anyone who disagrees with his ideas. In Season 2, we don't see these things changing - not even a little. As I said, we see him getting worse and worse in all of these aspects. In "A House Divided", he is introduced again as the short-tempered guy who won't fully accept your team. Of course, we are talking about a zombie apocalypse, we can't expect everyone to be calm and to be reasonable all the time, but Kenny goes to extremes and doesn't seem to learn from his mistakes. Lee is a good example of character who was easily pissed off in some situations and could be aggressive, but knew how to deal with people if the situation asked for it. Even Lilly, who was bossy AF, was more flexible than Kenny: she will forgive Lee even if Lee treats Larry like crap.

Being loyal is not the only quality that counts in this situation. Knowing how to be diplomatic is also important, maybe even more, since you have to live with groups to survive most of the times. Kenny is capable of heroic acts/capable of saving people, sure, Season 2 shows that, but this is something we already knew by the end of S1. Season 2 doesn't show him getting better when it comes to dealing with groups tho, which was the major issue/flaw in his personality. This is the opposite of character development. And I'm focusing on Kenny's mistakes and flaws because we are especifically talking about him. Arvo is a POS, Bonnie and Mike suck, sure, but I'm analysing Kenny, especifically. And the difference between Kenny and a lot of characters, I think, is how Kenny is constantly and consistently repeating the same mistakes.

Lilly is a psycho because she stole the van? Let's not forget that by the time that happened, she had a mental breakdown after seeing her father's head being smashed with a saltlick. If Kenny's tragic story makes you more compassionate towards him, I think it would be fair to do the same with other characters.

EDIT: One more thing that didn't cross my mind before. Somebody told me on Reddit they like Kenny, but decided to kill him to put him out of his misery. He lost his entire family and girlfriend, and now would have to live with the burden of being a murderer. The person told me they didn't think Kenny wanted to be alive anymore, but was living just for the sake of living. I still don't know what to think of it, but I think it is an interesting perspective. If you let him live, what is Kenny's future? Join (and cause trouble) to another group? Alone and depressed for the rest of his life?