He would have never intentionally hurt her or AJ. That much is clear. Kenny's only a loose cannon when provoked, and Jane was pushing him to his limits, very cruelly. He's a mean SOB, but it's only because he worries about what may happen to those he cares about. You can't blame the guy for his temper. His temper could one day potentially cause too much trouble that it may result in deaths, but that's only happened with Jane, because he thought she killed the baby.
Jane let herself in for the trouble with Kenny, because she pushed him. Though Jane DID try to stop the fight by putting her knife away, and she did say the baby's death was an accident. Kenny didn't listen and let his temper win out. He let his negative feelings towards Jane win out, so he just concluded he killed the baby, only because she seemed to care only for herself.
Jane WANTED Kenny to overact, and she knew he would. So she wanted him to leave her and Clementine. Did she do it with the the intention of killing him? Perhaps. Which was hinted at. That was pretty low.
Kenny's recklessness stemmed from his desperation to keep Clementine and AJ safe. I guees it's a no won situation for him. He's reckless in his temper and reckless in his caring. I guess basic human emotions have no place in that world anymore! You have to be cold and ruthless to be accepted
