Not that I know anything about your granddaughter, but if it is
stubbornness that's causing her to not speak, everybody needs to just
back off.
When someone is stubborn, pushing them will accomplish nothing. In fact it'll just make them more entrenched. I should know. I am stubborn and come from an entire line of stubborn knuckleheads. We won't even listen if we don't feel you're essentially on our side.
From the perspective of a stubborn knucklehead, the moment people push me to do something, it becomes harder for me to really know what I want to do, so the safest course of action is to dig in my heels until they lay off me long enough for me to make up my own mind. And I will stash all of your arguments to mull over in my own good time. I may come out agreeing with you and your recommended course of action, but as long as you push me, I may not be able to get to that place.
Perhaps she will talk, once her not talking is accepted. Why not treat
her as a non-talking person, since that's who she wants to be right now,
and embark on a study of ASL?
There's a wonderful web-site where one can study it free -
http://lifeprint.com/ - and it's got short videos of everything. At the
least it'll give you all some communication tools that could even be
useful in other settings.
A college friend of mine did not speak until she was five, and then she spoke in complete perfect sentences, using an extensive vocabulary, slightly ahead of her age group. When I knew her, she was a circumspect talker, a trait I have always admired, since I am sometimes an indiscriminate chatterbox.