A web browser plug-in called clea.nr helps with this problem by showing just the video itself on a plain white page. Here are some screenshots that illustrate the difference.
Regular YouTube, without the clea.nr extension:
Now here is the same video, with the clea.nr extension activated. Notice all the beautiful, uncluttered white space around it.
To get started, go to http://clea.nr, click on Extension, and then click the giant button. This will add the extension to your current browser. Then, when you go to a YouTube video, you'll see just the video, not all the stuff around it. The browser extension is free, and works with Chrome, Safari, and Firefox. (If you are still using Internet Explorer, you really should switch to one of these other browsers.) Clea.nr also offer iOS apps for a small price so that you can get the same features on an iPod or iPad.
Hopefully you will find this useful for sharing YouTube videos with children.
