Moving your main site to another host but clients on main NS's

[demomen]

Hey Guys,

I would like to do the following:

I currently have the main hosted website on the main servers IP, lets call it server1, and the nameservers are: NS1.MYWEBSITE1.COM & NS2.MYWEBSITE1.COM.

Now what I would like to do is move the main website from server1 to another server, not currently owned by me but just on another reliable third party host.

The problem is when I change the nameservers of my site it will change the clients websites.

Why? because there nameservers are all directed to NS1.MYWEBSITE1.COM, NS2.MYWEBSITE1.COM


So how do I overcome this; should I ask them all to change to the new area I have set on the server1, called NS1.MYWEBSITE2.COM & NS2.MYWEBSITE2.COM (set to my server1's IP) - or is there a much easier solutions