If you want to cover yourself, you have two options.
1) Video documentation regular of child behaves to show what he does - with date stamp. And follow up e-mail every time for paper trail to parent and attach video clip. Keep all e-mail and video.
2) Get rid of this client - serious. If you are worried about having to justify this child's injurys then only you can protect you. It not worth a few bucks an hour to ruin your reputation or to put yourself in position of weakness. You can't help everyone.