Option 4 would be to sell the child's iDevice and switch to Android or even Windows Phone.
This is a frustrating problem and it's hard for me to imagine any real technical reason for it. I'm quite certain Apple employs plenty of folks smart enough to solve the problem, so I believe the issue is driven purely by marketing - yet another way for Apple to sell more devices.
There's no good reason my under-13 child's iPhone can't trigger an email to the address associated with my apple ID requesting permission to buy an app. The email would include a link that I could click, triggering a push notification to my child's iDevice and allowing the download to proceed. No need for a second iDevice.
By the way, I'm new to this forum. Can anyone recommend a way to make such a suggestion / request to Apple?