Make iPhone apps think no external monitor connected
It Works!

I installed Flex per @AndrewLarsson and entered the name of the app that was detecting the external display.

I then went under UIKit, then searched UIScreen and returned pass-through on displayOut_actualScreens.

When I tested it with my AV adapter, the app did not know that there was an external display connected!

Many thanks to @AndrewLarsson for his help! Without it, I couldn't have figured it out.

UPDATE: False alarm. It wasn't working. I had gotten overly excited and missed the fact that IT DIDN'T WORK!!! I'm really sorry about that...