Are there any good mobile apps for teaching kids mandarin?

Plenty. Kids way to Chinese https://itunes.apple.com/us/app/kids-way-to-chinese-yct-1/id624614749?l=es&ls=1&mt=8 DoodleChinese https://itunes.apple.com/us/app/doodle-chinese/id400579904?mt=8 Just do a quick search in the iTunes App store and you'll find more results.