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You should certainly file the appeal just to have the process reviewed, and you should raise the issues within your family as a basis for reconsideration. If you were close to making the goal or showed improvement, then you have a reasonable argument to make. It's not an argument that will legally compel a different outcome, but it puts you in the position to at least ask for a different outcome.
The fact about the supervisor not reiterating the possible outcome isn't useful to you. If the Original discussion and the WIP indicated that reassignment, demotion or termination were possible, then there isn't any legal requirement to give ongoing updates that indicate that those are still a possibility. It is a good practice, but not legally mandatory.
I didn't really touch on that, because it's not useful to you and could actually hinder your argument going forward.
While gambling is a very real addiction, it doesn't give you the sort of argument you need to put forward in terms of any sort of ADA argument. Any sort of addiction can be protected, but only in the sense that you can't be punished for seeking treatment. Let's use alcohol addiction as an example, because the case law is very clear there. You can't be fired for needing time off to go to rehab, but you can be fired for missing work due to being drunk.
Treatment is protected...not the consequences of our addictions and how they effect our work productivity.