Hey 111122223333,
Syncing music with iTunes will be disabled while iTunes Match is enabled on your iOS device. So if you have Match enabled on your child's iPod Touch, you'll want to disable it in order to manage its music using iTunes and your computer.
To disable iTunes match on your child's iPod, go to Settings > Music and make sure the iTunes Match switch is set to Off.
via: iTunes: How to add a computer or iOS device to iTunes Match
http://support.apple.com/kb/ht4913
Then, to sync using your computer's iTunes libraary, you'll want to follow these directions:
iTunes: Syncing media content to iPod
http://support.apple.com/kb/ht1351
Regards,
Delgadoh