Option one: Since you are part of a group and other parents are there every time, I like your idea of speaking privately to the other parents. I hope that a group of you can go to her together. If just you alone go to her and say this isn't working, she can brush you off and think "This is just one cranky mom." But if a group of her clients comes to hear and says there is a problem, she cannot ignore you nearly as easily. This option means that you will just have to get over "feeling weird about speaking to the teacher" as you mention. You are a paying client and are not getting what you feel you pay for. Don't let her intimidate you, and the other parents should not either. Present a united front but don't criticize her child openly or she will probably get huffy and offended. Just be direct and simple. Draft a script of what you and others will say when you meet with her and don't have any kids there when you do see her.
Option two: Summer is a natural time for a break. Consider telling her that your son is taking the summer off her lessons - and then get him into a different format, if she is the only Suzuki teacher around. Have you checked recently to see if possibly there is indeed another Suzuki teacher in your area, maybe since you started with her? If you can't find another Suzuki teacher, try him on individual lessons with another teacher but be sure it's one who (a) is experienced with kids his age and (b) isn't going to be anti-Suzuki and try to have him "unlearn" things. You might find he thrives just as much under another teaching style if that teacher is good with kids his age.
Option three: Since he seems to be thriving and the issue with the teacher's kid is really your issue and not his -- Let it go, and just leave things alone. If he's pretty young, your son is still learning a lot. If your son, and not just you, is saying that the teacher's son is a distraction, then yes, you need to act on it.
I do agree that what she's doing is inappropriate at best and damaging to her business at worst.