Host records exist for a single resource then DNS will present names to clients as a list, the order of the list is rotated (Round Robin).
You could safely remove the DNS servers from the other NIC, it won't effect name resolution. But it also won't help with the name being added. If you wish to stop the name registering in DNS you might take a look at this KB article:
http://support.microsoft.com/kb/246804Under "Forward and reverse per adaptor" since the little tick box in the GUI rarely does what it's supposed to.
Chris