"The OP does not say why the iPad was in reach of the child, so we are left to consider different possibilities. If 100 different children throw 100 different iPads owned by 100 different nannies, I think that it is possible in 1 or 2 of the cases the Nanny shares some of the blame."
The problem with this is that you're arguing an edge case, but you stated several times that the nanny should be shouldering some of the responsibility, and those two things don't match. If it's "possible in 1 or 2 cases" out of a hundred, then you're acknowledging that it's extremely unlikely that the nanny did something that would warrant making her pay for any of the damage, so it rings hollow for you to say "We are talking about a Nanny who possibly should have known better than to leave an iPad within easy reach of this child.We are talking about a Nanny who possibly should have known better than to leave an iPad within easy reach of this child" because that's going to cover many of the 98 or 99 cases as well. I agree that it would be reasonable to ask the nanny to be more cautious with such things in the future, but in the face of this one example, saying, "...I would think carefully before leaving them alone with my child again" still strikes me as assessing too much of the blame to her.