If you had supplied your actual domain names we might be able to write a better reply for you, because we can use tools to look at the DNS of your domains.
I think what you are saying is that BOTH mysite.com and existingsite.com are already here at dreamhost, but “pointing live domain” in the first line makes this confusing because typically that would be talking about an “existingsite.com” that is hosted elsewhere. It also sounds like you are following the directions for when DNS of “existingsite.com” is not set to dreamhost.
If existingsite.com is hosted elsewhere the point that you are missing is that the mirror that you want to create is to a free and temporary dreamhosters.com sub-domain.
If existingsite.com and mysite.com are on the same server, then you don’t need those sets of instructions at all. Just make sure that existingsite.com and mysite.com are set up using the same user on “manage domains” page in the panel. (look for the “web hosting” collumn) and then just beneath the words “fully hosted”). If both sites are using the same user there then when you are ready to make the new site live there it’s a pretty simple set of instructions, but to tell you EXACTLY what to do there we need to knwo what webapp you are using such as wordpress or phpbb etc (the wordpress instructions are in this forumm many times.)