How to Explain 'me' and 'you'?

It's a little embarrassing to say that, whilst trying to explain something to an 18 month old this week, both Simon and I came up empty handed.
I don't think it's unreasonable to say that Isabelle has a very good vocabulary, and her speech is much further on that I would have expected at 18 months. She regularly strings 4 - 5 words together, and sprouts words that I have no recollection of using with her in recent history (today it was 'castle' - where did she learn that?!)
We haven't taught her very much at all, really. Like all toddlers she has simply picked it up as she goes along. She is, by nature, a total chatterbox which I think has definitely had an impact on how quickly she has expanded her vocabulary. By nature, I am also a bit of a chatterbox, so the poor child's ears are exhausted from listening to me and no doubt she is just working up to saying "Mummy shut up!" some day - which actually wouldn't surprise me, after she told me "Mummy, move" earlier this week.
However, this week we stumbled across a sticky point. Isabelle refers to herself only in 3rd person as "Izzy". If you say "Whose shoes are these? Whose plate is that? Who was just about to draw all over the wall?" she responds "Izzy". So, we thought it was about time she learnt the word "me" and it's close partner "you".
However, that has posed a bit of a problem. How do you explain - to an 18 month old - what 'you' and 'me' mean? It is almost impossible! Simon tried first, and came up with nothing, only managing to get himself confused in the process. I decided the next day I would have a go. The conversation went something like:
Me: And who did that?I: IzzyMe: You can say "me". So when mommy says "who did that" you say "me" (and I pointed at myself)
At this point, Isabelle pointed at me and said "Me!". I accidentally taught her that 'me' means...well...me. Not her.
Me: No, no, you are me. (I pointed at her)
So, I'm sure you see the problem. To me, she is 'you' and I am 'me', and when I try to explain that I say "You are me" which just makes no sense at all - like much of this post!
To an older person, of course, it wouldn't be tricky to explain, however to a tiny tot with a limited grasp of English (but a superb grasp of gibberish) it is extremely difficult. I know that it is something she will pick up in time, as she has done with all her other words, but it has left both Simon and I just a tad confused and feeling a bit out of our depth. If we can't explain two such simple words to her at 18 months, how on earth are we going to see her through education until 18 years?!
(PS, don't forget to enter my competition to win a ByElsieB personalised cushion here)