Like the person below me said, the app works great as long as you have the guided access on.. that disables the home button.
Settings>General>Accessibility>Scroll to bottom>Find Guided Access>Turn it on and setup 4 digit code. BOOM just fixed the problem.
Now when you have the app open (which has loads of cute videos for your little one btw) you just hit the home button 3 times and enable the guided access. That combined with the apps full screen lock = baby not being able to exit the app OR pause the video.
Tiffanyjae89 about Baby Lock