My Horizon 40AD has the kitchen on the large-slide... driver's side.
I have a floor plan of a 40KD and see your kitchen is on the short-slide... passenger side. This slide is called an X-Slide because of its articulating arms; and there is a chain link that has been known to jump a tooth.
This being the case, maybe this information will be of some assistance.
Note: I have never repaired my X-slide so please keep us posted on how you do it.
I did find this video that may also be of help to you and others if you have chain link problems: