You can redirect from site A to site B by means of 301 command (that have to be done by your host company)or from page A to page B by means of a javascript redirecting page command.
You can also "park" domain A on domain B without redirection:it will visible the "parked" one (domain A).
Look at something like "register DNS" or "create DNS" , etc.
E.g. for Enom you have to go to the menu at the left, select 'domain names' and then 'register DNS'.
Use the tool in the first section of the page "Register a Nameserver Name" to create your nameserver.
Of course, the domain mydomain.ext must be in your account.
I think you should be able to point the names to the real nameservers' IP addresses without "them knowing" it.