Google distributes massive amounts of personal data to governments. They are not privacy friendly., and this affects trustworthiness, because people expect privacy from Google.
Many sites now refuse access to Googlebot, because of the privacy issues and concern about Google's expansion. This reduces the reliability of their results.
Even with SafeSearch on, Google is not an appropriate search engine for children. Children should use a Child Oriented search engine, where each site has been visited by a human to determine its suitability. (I am not endorsing them, but kids.yahoo.com and netnanny.com are options).
I cannot rate Google very high on privacy since they add cookies if you don't block them and track you all over the web. In addition, they keep a record of all your searches. As for child safety, keep an eye on what your kids are looking for because Google won't.