The rented movie's avatar shows but no actual movie - any ideas?

Have you tried selecting the 'avatar' to play the movie - has it adequately downloaded? Is the 'play time' actually telling you how long you need to wait until it'll play? If so leave it on that screen as playing other things/previews will reset the download to start from scratch.

AC

You rented on the iPad not the AppleTV? You are playing from the iPad to the AppleTV via Airplay?

AC

Sounds like an issue with Airplay, most likely due to a networking glitch.

I'd restart the AppleTV and iPad and try again.

Why did you not rent on the AppleTV?

AC

I'm not certain that Home Sharing has a big effect on Airplay (which after all would be far less useful if guests could not Airplay to your AppleTV), but if your AppleTV is configured for Home Sharing with a different account you could try changing the Home Sharing account in Settings on AppleTV.

Has she restarted the iPod (Touch?).

AC