Where to find the option to start a separate (second) tax return for my underage child?

Are you using the Desktop install program or the Online web version? 

You can start another return in TurboTax Online by:
Logging out if you are in your account
Choose what TurboTax Online product you want to use for the second return
https://turbotax.intuit.com/personal-taxes/compare/online

Create your account screen
Set up a new login for the second return
Start working on the new return

If you are filling online, you would setup a new tax return with a new ID and Password.

Select [Start for Free] on the TurboTax Website.