I cannot affford a lawyer but would like some help in where to locate the laws myself.
Unemployment qualification decisions are most often set by case law. The cite given in the last post is a great example (a precedent) as to why I believe you are facing an uphill battle. All you can do is appeal (until all appeals are exhausted) and give the facts of your side of the story, and the employer will do the same. I've never had to deal with UI in the Commonwealth of Kentucky. However, in many unemployment hearings I have sat in on from the employer's side, I have generally found the hearings administrators (called diffrent titles in different states) are quite reasonable and objective. They are very skilled at bringing things back on track if either side gets side-tracked or begins to behave inappropriately.
Where I see your issue (especially in light of the cited case) is that, in a way, you did sort of quit in anticipation of termination. You not only took the rest of that day off for "mental health" but also the subsequent days. That could be looked at in many ways. One could even look at it as though you were trying to use up all your sick days in anticipation of termination. Furthermore, although the employer indicated the complaint could lead to termination, the employer had not actually terminated you yet. There was a possibility that things could have been worked out.
Your post does not indicate whether the supervisor actually listened to the call (sometimes - or even often-- call center calls are recorded). If s/he hadn't listened to the call, then s/he is just dealing with the caller's complaint. If it were the latter, you may have been given an opportunity to further explain the issues, where you may have been at fault, where you may have been right, and whether the caller was just plain rude. (Depending on the type of call center, some customers can just be nasty and complain when they don't get the answer they want.) On the other hand, the termination could have been inevitable, but it was still on you to stick it out.
I wish you the best of luck in your appeal, but also hope you learn from the experience. If you lose the first one, you can keep appealing up to KY's limit. Please understand, however, that if you win the appeal, the employer can also continue to exhaust all permitted appeals.