I have tons of info on "My Calendar" Galaxy S3, and Google Calendar sync is one-way only. I actually use a Yahoo email and would prefer to sync both ways to Yahoo or Google, but since I cannot find a solution to this, I just need a backup that I can run periodically. Please help!
You can use Samsung's Kies program.
The link below describes some details of the program. It includes backup of calendar as well as most other content of your device.
What about to enable the Sync options into Account options in your mobile?
You can go to "Settings>Accounts>[Your Google/Yahoo account]>Sync Calendar"
If you touch the option "Sync Calendar" the sync are made once, but you can enable sync automatically selecting the three dots in the top right.
To check your data was sync, you can login into google account and go to the Google calendar Here you can see all your data.