Mirroring live AD enviroment in a Lab enviroment

I am planning to mirror my live AD2003 enviroment in the lab but i have some questions

1)how do I avoid any conflicts it creates when the lab is connected to the internet (some of my systems have external Ip adderesses)

2)how do I connect to the the lab network servers from my desktop which is in the live enviroment with going to the lab room physically (what is the best way of doing this)

I WOULD LIKE TO MIRROR LIVE IN THE LAB AS CLOSE AS POSSIBLE WITHOUT CHANGING ANY IP ADDRESSES

THANKS.