From what I can discern from question, you are actually looking for Video Mirroring, not Video out. They are two distinct features, using different API's.
Video Mirroring, i.e. everything that you see on your iPad screen, from home screen to various apps, is only available via Airplay, using an Apple TV, or using Apples Digital AV Adapter(HDMI) or VGA Adapter.
Video Out, which is what it sounds like you are currently using, is available with Apples Composite and Component AV Adaptors, and provides an output link for applications that are specifically outputting a video source, such as the Videos App, or YouTube. This would be why you can see YouTube Video's in YouTube, but not say when they are embedded in Safari.
You should also know, even Mirroring doesn't work for all Apps as you would expect. HBO Go for example, actively disables Video Mirroring and only supports Audio, so when you hook the iPad to your TV, all you see is and HBO Go Logo on your TV Screen. There is currently no official way around these restrictions.
An app is just a file. You can distribute them through a sophisticated framework such as a custom App store hosted on your own servers or just place them on a web server. In fact, you could also just email the app or push them through iTunes or other file sharing technology.
When you sign up as any iOS developer - you can install apps on your devices without ever submitting them to Apple. In the case of an enterprise account, you are allowed to install them for production use as well as development use.
The mechanism you choose for Mobile Device Management will affect your costs and benefits for the various distribution methods, but your general question is answered - Yes, as an enterprise developer no Apple involvement is needed or possible if you don't want your apps ever on the App Store in general or getting reviewed by Apple in specific.
Best Answer
On a non jailbroken iPad you NEED to enroll iOS Dev Program, which cost 99$/Year and then use Xcode.
Cf : https://developer.apple.com/programs/ios/
There may be other frameworks that work without jailbreaking and/or Xcode.