That's a tough one.
The problem you have it that you have a pretty substantial crack that is always going to be susceptible to water. Having said that, it looks like it dropped to the bottom of the photo you provided. Something is happening in that corner to cause it to drop. For that level of crack and height discrepancy, you almost have to have a grade issue that I would want to address before I did anything. You really have two choices. (at least IMO, hopefully somebody else in the concrete industry will chime in.)
1. Mud jacking technology has gotten better, but keep in mind you will have to fill the crack and if you have grade issues like I mentioned, it may not be long before you have the same issue again.
2. Have somebody demo and repour that section. They could put a joint in front of the rail and wherever they chose to start. I would be interested in seeing the whole pool deck, if possible. Are there any existing expansion joints that might provide a starting point? I would make sure I had somebody who has done this before. The problem you have is this is a small job so alot of the more stable/reputable concrete guys are gonna not be that interested.
Any type of overlayment will likely be too thick to be durable and if it keeps sinking, won't address the problem.
Like I said, first thing to do is figure out what happened to wash out the corner that dropped.
