To me, Death doesn't necessarily mean The End. It can be about change in general. For example, there might be a break-up, but not the sort where people don't speak to each other ever again -- I've had friends who have broken up with each other but became best friends after that, they just work better on a platonic level. It could be about other changes, where the relationship remains but something is different, for example, they start ressenting each other but don't break-up, it becomes long-distance, or it goes through hardship and becomes stronger. There are so many types of relationship changes that I would consider possible.
With the Knight of Swords, I would still consider that it doesn't have to be the end -- just very fast changes and a lack of stability. An argument that escalates, a sudden move, things like that. On the other hand, it may also mean that those changes will be over quickly, for better or worse. Given the association with swords, I would say that it's probably more related to thoughts than feelings. It's a relationship reading, so some feelings are unavoidable, and it doesn't mean they're rational thoughts. But I would say there is a difference between change happening because a partner suddenly falls in love with someone else, and change happening because that partner starts thinking about the relationship and thinks that make them unhappy.
I hope this makes sense, and it's just my two cents. The horses on the cards make me think of some kind of collision or obstacle, but that's a wild guess on my part.
