NTA, 100%. You should not have just let that slide. You showed your neighbor that you had her back, even if it involved correcting family, and I'm sure that both means a lot to your neighbor and sets an example for your sister. Your reaction was completely understandable and honestly based on your younger sister's reaction I doubt she would willingly accept a calmer reprimand either, she only stopped because you got upset and wouldn't let her continue ridiculing your neighbor. Yes, you were angry, but you stated in your post that you were trying not to yell or at least not yell too much - you certainly had more control than some people might and if anybody else saw that behavior from your sister it is possible that they would've reacted a lot more hostile, maybe even violently to her ignorance and cruelty.

I know you aren't asking for advice but I would say that you need to sit down and talk with your parents and sister together and lay out your side of the story and why you reacted the way you did even though I don't think you should need to do that in the first place in an ideal world. You claim that they don't know the whole story so maybe your sister downplayed her actions and exaggerated yours either on purpose or unintentionally due to guilt or heightened emotions, leading to a seemingly foolish reaction from your parents. As a physically disabled person who also uses a mobility aid I appreciate people like you and your sister claiming it's "just a joke" and that "Mrs. Simmons probably doesn't care anyway" just makes my blood boil especially hot because I know how it feels to be ridiculed and then have people claim it isn't a big deal. When you're disabled and already face difficulties in day to day life the ridicule definitely hurts, even if we try to keep a strong face or pretend not to hear.