Where is the option for sd card?
Even if you store Youtube video in internal, You can't use it without youtube app.

Youtube app is not a video pleayer. It is Video Streaming app.

It streams packets and The video is splitted to parts and stored in Youtube data files.

When you open it, it is actually getting Streamed rather than played.

So, if you store it in sd card, youtube won't detect the files and will not play the video at all