Hi, my name is Britton. Sorry to hear about your sister, here is what I recommend:
I like to use keepvid to download Youtube videos:http://keepvid.com/Copy the URL (i.e. http://www.youtube.com/YzGHua...) from the Youtube video and paste it into keepvid. I like keepvid because it allows you to down the video and save it in MP4 format. Normally, Youtube videos are all in FLV format and will only play in Adobe's Flash Player.
Once you download the videos you want from Youtube, you can burn them to DVD using Toast. The downloaded Youtube videos will show up in your Downloads folder
Let me know how this goes...