The latest version of Mobicip works using VPN, and so is now able to filter the native Youtube app. Just setup Mobicip on your child's device and you are good to go.
Mobicip filters YouTube by reviewing the title, description, comments and other meta information associated with each video. In most cases, the publisher would include suggestive words and phrases with the video and it would be blocked by Mobicip. Like any filtering product, Mobicip filters the content on a best effort basis and goes beyond most other products in terms of the quality of filtering. Mobicip is the only filtering product that offers YouTube filtering on a video-by-video basis. So, please try accessing the YouTube app and see its effectiveness in terms of filtering inappropriate content.