Did you take your time to look at the question2answers Addons here: http://docs.question2answer.org/addons/
There is a plugin for that Called Embed Youtube Plugin by NoahY that converts links to YouTube videos into embedded videos when displaying questions, answers or comments.
Download it from https://github.com/NoahY/q2a-embed
Please try out the modified version of Embed Youtube Plugin from https://github.com/gurjyot/q2a-embed by Gurjyot Singh. It should do you good.