I agree that fighting this with a lawyer is likely to end badly for you. The courts are very clear about academic privilege for schools. Unless you can prove that you were actually discriminated against (and nothing so far in this thread is proof of that), courts will defer to schools. All you will do is make your school angry.
There is unlikely to be a "second appeal". You could look at your school's "student manual" (they probably have a different name for it) and it should explain the process. If there is a second appeal, it's probably the Dean. The chances of the Dean overturning the findings of a clerkship are very small.
Regarding your fluency disorder, you've already hit the high points. It probably counts as an ADA disability -- although if it doesn't affect other parts of your life much, it might not. If it does, then you need to ask for accommodations before you run into trouble -- you can't ask retroactively. Accommodations would be "what can the program do to help address your disability?". They won't change their standards -- you're still expected to see the same number of patients, meet duty hours, etc. Asking to see less patients, or more time per patient, would not likely be considered acceptable. Still, best to get it evaluated by the disability office and see if there are any options.
Regarding the comment "does not have issues with speech", it's probable that what's meant by that is that your mild speech problem is not the cause of their concern. I agree it's worded poorly, and it's possible that the evaluator misinterpreted your speech problem as a social awareness problem -- but I find that somewhat hard to believe / explain since the two are very different. Asking why your school "won't support you" because of this statement is missing the point, I think.
Like many threads like this, the story may get more clear as the thread progresses. You wrote above that your behavior may have been very irritating to the residents, and maybe to the faculty as well. The faculty member just dumped you with the dentist to hold things, which is ridiculous. But is probably due to the fact that you were driving people crazy. Seems likely unrelated to your stutter. That's the real problem here, I think. Once you create a problematic persona for yourself, it's hard to change.
But what about those nice things people said about you? First, they might very well be true. You may have only upset some people, and not others. Or perhaps your performance was variable - better on some days than others. Or perhaps those people were just too nice, and wrote something bland so that they didn't have to write about the real problem. This is a very common problem -- it's rare that all of the comments are problematic, so even if only a few are it may represent a real problem.
Underlying all of this is the problem that evaluation in medical school is subjective. Hence, it's amenable to bias and error. If someone finds an objective way to actually evaluate clinical work, it would be great. But it's probably impossible.
Anyway, the core problem here is that you really upset the people you were working with by not understanding the workflow, your role as a student, and how you can be helpful. You may argue that they should have taught you that as part of the rotation, others would argue that it's something that you should have picked up by now (most schools have some clinical work early on) or that you should have picked up on the fact that you were annoying people very quickly and fixed the problem. Faculty and residents don't get paid to have you work with them -- students slow us down, so you need to either 1) find a way to be useful and save me some time, or 2) be fun to work with so that I don't mind the extra time / work.
I hope this is helpful.