Kids who do the best after divorce have parents who put the kids first. (Easy to say, much harder to practice.) By treating their ex-spouse with respect, never putting the kids in the middle, ( with nasty comments, quizzing, that sort of thing) and working together as a team, parents can really make a difference in how a child processes and experiences a divorce. Of course, if the parents can't control their emotions, the opposite is true.
Here's hoping Jon and Kate are willing to do the extremely hard work of being parents first and foremost for the long term emotional good of 8 kids.