I would try two things. First reset your iPad but close the YouTube app completely first.
In order to close the YouTube app, drag the app up from the multitasking display. Double tap the home button and you will see apps lined up going left to right across the screen. Swipe to get to the app that you want to close and then swipe "up" on the app preview thumbnail to close it.
Next, reset the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.
IF the app still crashes on you after you try this, delete the app and download it again. Hold down on the app icon until it wiggles, then tap the X on the icon in order to delete it, tap the home button and the apps will stop wiggling. Then go to the App Store purchased tan, find the YouTube app and download it again.