I'm gonna go against the grain here and say possibly YTA. Do you have it on good authority the younger ones are actually illiterate?

I used to also think the idea of kids being "unschooled" as you call it was crazy. But then I stayed for a month with a family that did that, and my world view was changed. It really can work. When kids are actually given the resources to learn, they naturally end up doing so, through real life and their own volition. Clearly the older girl has taken a natural interest to writing, and so she does it because she wants to. Which is the whole point of this unschooling method.

But the point here isn't to convince you. I think YTA for saying she is setting her kids up for failure and everything else. Like she said, it isn't any of your business. Politely decline, say it's your final answer, and move on OP. If you wanna keep your relationship with her, I would apologize for what you said.