Trying to use feature LOG_FGDN ON which performs a nslookup in ac cess.log

My configuration is a SQUID 2.1 RELEASE proxy server proxy.mydomain.com
under Linux which is
connected on a primary interface onto the local private network, which has
already
a DNS server dns.mydomain.com for mydomain.com. This private DNS is NOT
connected onto the internet.
My proxy.mydomain.com is also directely connected onto the internet via a
second interface card, with a DNS server from my ISP.

I want proxy.mydomain.com act as a DNS cache for these two interfaces, so
i use named.

1. On one hand, i am able to resolve classical dns internet cache with this
config :
########### named.boot ###################
directory /var/named
; type domain source host/file backup file
cache . internet.cache
primary 0.0.127.IN-ADDR.ARPA 127.0.0.zone
primary localhost localhost.zone

########### internet.cache #################
. 99999999 IN NS ns.internet
ns.internet 99999999 IN A 194.2.0.0

########### 127.0.0.zone ##################
@ IN SOA proxy.mydomain.com. me.mydomain.com. (
            1
            360000
            3600
            3600000
            360000
            )
     IN NS proxy.mydomain.com.
1 IN PTR localhost.

########### localhost.zone #################
@ IN SOA proxy.mydomain.com. me.mydomain.com. (
                  1
                  360000
                  3600
                  3600000
                  360000
                  )
           IN NS proxy.mydomain.com.
localhost. IN A 127.0.0.1

It works OK for the internet.

2. on the other hand, i am able to resolve names on my private network only
with this config:
########### named.boot ###################
directory /var/named
; type domain source host/file backup file
cache . mydomain.cache
primary 0.0.127.IN-ADDR.ARPA 127.0.0.zone
primary localhost localhost.zone

########### mydomain.cache #################
. 3600 IN NS ns.mydomain
ns.mydomain 3600 IN A dns.mydomain.com

It works OK too, but separatly.

My problem is that i can't find a configuration where i can resolve the
two networks at the same time.

I've tried this:
########### named.boot ###################
directory /var/named
; type domain source host/file backup file
cache mydomain.com mydomain.cache
cache . internet.cache
primary 0.0.127.IN-ADDR.ARPA 127.0.0.zone
primary localhost localhost.zone

with this new mydomain.cache:
########### mydomain.cache #################
mydomain.com. 3600 IN NS ns.mydomain
ns.mydomain 3600 IN A dns.mydomain.com

but it doesn't seems to work.

I think i've missed something. I hope i gave enough details that
someone can help me with it.

Thanks on the time spent answering

--
Paix sur terre aux hommes (et aux femmes) de bonne volonté.