No, I'm afraid we can't allow this. That YouTube app is Apple proprietary software and, as such, is protected under their EULA. There is and will be no exchanging of software here.
In addition, as the YouTube app was a system app, it's not a simple matter of getting/copying the .ipa (as there would be with a "regular" App Store app).
Have a look in the App Store for the free YouTube app. It's the "official" Google one and I understand it works as well as the stock Apple one ever did (maybe even better).
All that said, and since we can't/won't help - I'll close this thread. Thanks for your understanding.