Why can't you use the Youtube Url and stream it using WPF MediaElement control? In that case you would have fool control on the Player.
There are 'n' number of Youtube Video downloader. If there can do it, streaming should be possible.
But make sure you read the copyrights policies of Youtube before streaming.
Update:
Already Sacha has an example for you,
Stream YouTube Videos in WPF[
^]
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