From an emotional and storytelling aspect, this story worked for me. I followed along and was interested throughout. But I did not find it plausible at all - just too many places where my disbelief was stretched beyond breaking point. She is physically limited - she can't climb or pick up large objects - and she is apparently incapable of the motor control necessary for a computer touchscreen interface. But she was somehow able to find pictures of the human vocal system? Did her parents just leave them around her room? If she could google image "vocal folds", she could also write "hello dads" on the tablet/computer.
Also, even now there are special touchscreen and computer interfaces available for children with motor disabilities. I cannot imagine that in this future there will be no special interfaces designed for people for whom normal gesture recognition doesn't work.
And how in the world did she learn to spell? Or indeed, learnt the word "tardiloquous"? You can't just pick up English words and their spelling by being intelligent - you need to be exposed to them. And I assume that her parents weren't just leaving books containing words they probably didn't know within reach in her bedroom.
Finally, and this was brought up by others here too - what happened to all the doctors/speech therapists/child psychologists in this world? Didn't anyone ever think to look down her throat? Or to figure out a means of communication that does work? Again, I know people who work with communication with severely disabled children. Even when the parents can't think of ideas, there are professionals whose job it is to try every avenue of communication. Did no one think to ask her "do you understand me? whistle if you do. Great! Now, make two short whistles followed by one longer whistle", and then you at least know that she's aware and can understand English, and at the very least, teach her to whistle in morse code or something.
Maybe, if Charlotte was unique, I could buy that her parents just couldn't afford proper care and the doctors she saw just ignored her. But if this is common enough that she could meet a second child with the same symptoms, then presumably someone studied these cases. And trust me - if there's a new speech impediment that affects even a small amount of the population, there would be doctors, researchers and others jumping at their chance of being the one to find a treatment that works - not for altruistic reasons, but that's because that is how you build your career.
So yeah, overall - a decent story as far as stories go, but seriously (in my eyes) hurt by its lack of plausibility.