As a committed amateur musician, I'll remind you that the word "amateur" means "a person who loves something." You led with the fact that your son loves the viola, and that is something that should be supported -- I think it's okay, or even important, to show a gifted kid that you're not required to be the very best at something in order to have permission to pursue it passionately and work on developing your own skills over time and to just plain enjoy doing it.
Okay, so then we have a question of whether this teacher and/or this training method and/or this instrument is a good match for this kid.
Instrument: If his dysgraphia is focused around fine motor / graphomotor control, sequencing, and automaticity, (and from what you're saying about the overflow, I'm wondering if working memory is also lowish), then yeah, that's going to make viola (or pretty well any instrument other than percussion, as far as I can guess) pretty tricky. Note that he's got to coordinate two hands doing very different but related things, too -- that's extra hard, although I can't be all that confident that something like piano (where the two hands are coordinating on similar and related tasks), a woodwind (where the hands are doing the same thing) or a brass instrument (where only one hand is highly active) would be all *that* much easier. But man, a non-fretted string instrument... that's about the toughest thing going. And the most painful to listen to when it's not *just* right. Much as I would like to defer to his love of viola, I'm wondering if an alto or tenor instrument in a different family (clarinet, english horn, french horn, they all have the same kinda mellow-gorgeous vibe as viola, at least to my ear) might be a bit easier. If he can't hear the subtleties of pitch well enough to adjust on the fly, though, then I'd have to say maybe piano is a way better plan for success.
Method: Suzuki is a great method, but it's not for everyone. It does require a lot of coordination between "what you hear" and "what notes you therefore need to play" and "what movements need to happen to make those notes happen," and my sense of it is that it requires the kid to figure out much more pretty well on their own, although I know that teachers vary widely in their methodology. It sounds like this teacher isn't giving as much clear guidance and simple skills practice as your son needs -- too much gets piled on too soon. Perhaps a method which is a bit more explicit and skills-based, even if it doesn't sound quite as interesting at the start, might be, again, a bit better of a plan for success.
Teacher: This is crucial crucial crucial. And it sounds like this teacher is not quite getting him, and the relationship between them is starting to degrade as his skills don't quite keep up with expectations. I wonder if it would be possible to help get the teacher more on the same page -- you have seen this kid work hard and improve in other domains, so perhaps the teacher could become more comfortable and confident in working with him if there were ways she could be effective with him. Or perhaps in having the dialogue you and she and he can figure out that it's not a good match. I think I'd be careful in that dialogue not to frame it as "teacher failing with student" or as "student is so hopelessly bad," but just a question of whether she's comfortable working with a kid who may very well not progress at the rate or through the methods she is used to. This is going to be much more of a problem-solving process for her, and frankly, not every music teacher (or every any kind of teacher) is really up for it. She has to love (or at least be intrigued by) the process of teaching him.
My piano teacher, I have to say, this was her great talent as a teacher. She was very adaptable to her various students. She had very high standards, but she also was very sensitive to where each kid could reach at the given moment. She was clever in terms of coming up with specific drills to improve target skills without being boring. And above all, she was very tuned in to how each kid could approach music and find their passion for it. (I'm sorry to say she has passed on, otherwise I'd give you her name).
