To select which calendars to sync to your Apple device, follow these steps:
- Open the Safari browser on your device, it has to be your apple device, and go to http://m.google.com/sync
- Sign in with your account and select your device from the list of devices you’ve set up for Google Sync.
- Once you select your device you can choose from the calendars you have already set up in your Google calendar to sync.
- You’ll need to do this setup on each IOS devices that uses Google Sync, to show multiple calendars.
I also found this helpful link that list some of the known issues between Google sync and IOS devices. Click Here