Seeing that this is quite an old question and I've not found any obvious answers to it, I've just spent quite a bit of time looking at this myself... I eventually found that when the child account wants to request an app:
- Select the app in the app store (on the device the child account is signed into) to open the details
- Select "Get" (note: this must be done from the details view, not from the app list page, otherwise the option does not seem to be visible), then select "Install"
- Enter child account's password when prompted
- Re-enter child account's password if prompted again
- A message box appears prompting the child to "Ask Permission" - select "Ask"
- A bar will appear above the details with the following text: "Your request was sent and is awaiting approval from a parent. They can also approve it in person on this device."
- Here's the key: select (touch) the text that appears. It's not immediately obvious that it's a "button", but if you press on it, you are presented with an "Approve In Person" message box
- Now, when prompted, enter the guardian's Apple ID and password
- Enter the child account's password again
- The application should now start to download. (There may be yet another annoying password prompt af this time.)
Hopefully that helps someone in future. (Now, if only I can reduce the number of password prompts...)
