There is nothing on a jailbroken iPad that a restore to stock firmware cannot fix.
When you restore an iPad, you are, in essence, completely wiping the operating system and then putting a new one on. It's as if you wiped the slate entirely clean...
Nothing gets left over - it's as if you took the iPad right out of the box on a new purchase.
Since you are having trouble with YouTube on a stock iPad - it's not (and wasn't) the jailbreak that's the problem.
Marilyn