If Jack does succeed in changing things. Their relationships will still have happened. What Kate doesn't see is that nothing will be lost. Her present self will continue on; it is only her future self that will be affected. Let's say they are able to change something in 1977 but are still stuck there. Or even ebtter, they go back in time again even earlier. The Jack and Kate we know right now will still have all their memories. It is the future versions of themselves (the ones who will eventually get on 815) who will not experience the crash. And lets not forget about the universe, destiny, all that stuff. If something is changed, then 815 no longer "needs" to crash. The passengers are no longer needed on the island. So, destiny or the universe, might deal Kate a whole new hand of cards. One in which her father is not an abussive drunk. Thus, she doesn't have to kill. Thus, she doesn't go to jail. How about them apples?