I rang Apple support in the hope they'd be able to change my purchase to a "gift" instead. Long shot I thought but I had nothing to lose.
I got told they would normally charge to help as my i-pod is out of warranty, but the kind man waived it and helped me.
Once a transaction is made, he said that I couldn't change it to a "gift", but he did solve the problem for me. He said all I had to do was to get my cousin's computer authorised which she could do herself once she typed in my password and ID. So I rang her and stepped her through it this afternoon and now all those 9 episodes I bought and put on a disc are now working!
I've only ever "authorised" once (on my laptop) and that was a long time ago, so I would have taken me ages to find where to look for it or how to do it, but it turned out to be very easy as the Apple Man stepped me through the procedure. I've written it down now so I'll never forget again and now I know that "authorise" isn't just to see my i-pod, that's its about sharing as well.
Regarding Home Sharing: I wasn't able to get far with home sharing.
It will only work on computers within your house.
So all is now sorted and good!
