DNS and dynamic IP: help needed

[Name]

hi all,

I'm using a dynamic DNS to reach my site from internet: mysite.mine.nu 
(dyndns.org).
I want to setup on the lan a DNS server (linux debian) for all the 
computers of the LAN. The name of the computers will be 
computerX.mysite.mine.nu.
I user forwarders in named.conf

Here is my zone file mysite.mine.nu:

@       IN      SOA     dnserver.mysite.mine.nu. root.mysite.mine.nu. (
                         199802151       ; serial, todays date + todays 
serial #
                         8H              ; refresh, seconds
                         2H              ; retry, seconds
                         1W              ; expire, seconds
                         1D )            ; minimum, seconds

                 NS      dnsserver
                 MX      10 mailer.mysite.mine.nu.

localhost       A       127.0.0.1
dnsserver       A       10.0.0.1
computer1       A       10.0.0.10
computer2       A       10.0.0.20
mailer          A       10.0.0.30
mailer.mysite.mine.nu.    A       10.0.0.30

mysite.mine.nu.           A       10.0.0.10

computer5    A       192.168.0.10
computer6    A       192.168.0.20


The problem is:
# nslookup mysite.mine.nu
I get the answer:
Name :    nu.mine.nu
Address:  203.164.2.199
Aliases:  mysite.mine.nu.mine.nu

I want to get the answer: mysite.mine.nu 10.0.0.10 and not the answer of 
   my dynamic DNS (dyndns.org).

I read again the docs and surf the web, however I'm still missing something.

Any help would be appreciated.
Many thanx in advance.
Mike.