I cannot input an APO address for my child's child care provider

You can try the following:

 

When you are in the Child and Dependent Care Credit section of TurboTax and you are on the screen that says: "Let's get some info about your care provider", click on "Other" and more fields will show up.

 

You can get to that section of TurboTax as follows:

1. Click on the search icon in the upper right of your TurboTax screen
2. Type "dependent care" in the search box
3. Click on the link "Jump to dependent care"

 

 

Your TurboTax screens will look something like this: