Am I the only person who thinks the original sentence is actually possible (without the word "her"), if you consider that "She has to have had to" equates to "She must have had to ..."? Let's say the poor woman in the sentence has a dent in each side of her nose, the kind of dent you get from wearing glasses long-term.

- Have you seen the dents in her nose?
- Yes, they're very deep. What do you think caused them?
- She has to have had to wear glasses since childhood.

That would mean that in the speaker's opinion, the only explanation is that she has worn glasses for a very long time. That has to be the explanation.