I'm not sitting in front of my Premiere at the moment so I can't test this, but since no one has gotten back to you, here's what I would try (if you don't have one, I'll try when I get back home on Sat).
There is a sign in page on the TiVo youtube menu. Signing in there with a youtube account should give you access to your nephews new videos. In other words, create a youtube account, subscribe to whomever posts videos of your nephews youtube account, and then sign in to your youtube account from your TiVo. I'm not sure you can subscribe to a users account from a TiVo, but you can from www.youtube.com
I'm sure someone out there can try to verify this before I get back home...