go into your device settings, and find "apps" (I think it's under the "general" tab). Scroll down to find Chrome, and tap on it. Scroll down that screen slightly to find a "clear defaults" button. Tap that - anything that you've previously told to be opened with Chrome (any links or apps) will be cleared from memory. Don't worry - you're not deleting any personal data or bookmarks! All you're doing is telling the phone "Hey, anything you used to open directly with Chrome? Yeah - forget it. You have to ask again now!"
Find a Youtube link and click on it. On that menu that pops up - make sure the "Always open with" checkbox is NOT checked when it tries to open with Chrome. Chrome should try to redirect it to the YouTube app, and when that menu pops up again - make sure the "Always Open with" checkbox IS checked when you see that you can open it in YouTube. Hopefully this makes sense.