Linksys Wireless router, DHCP, DNS question

Hi all,

Here is the case:
(1) One DSL,

(2) One Linksys Wireless Router, with DHCP, ip address is 192.168.1.1,
dhcp range 192.168.1.2 -100

(3) One Linux DNS, ip address is 192.168.1.200, gateway is
linksys(192.168.1.1) and dns pointing to ISP's dns servers, in it hosts
file, there is one line as
192.168.1.200 dns1.mydomain.net dns1


(4) couple of winxp workstations connected to Linksys, get ip lease
from linksys, those ws names are msws1, msws2, ...

(5) couple of linux server/ws connected to linksys, get ip lease from
linksys
their names are lx1, lx2, ....

(6)In MS workstations' tcpip property, defined dns suffixes as
mydomain.net and DNS address as192.168.1.200 in addition to dhcp's

(7)In linux boxs' resolv.conf, add lines
domain mydomain.net
nameserver 192.168.1.200
#dns from isp
nameserver 204.yyy.xxx.1
nameserver 204.yyy.xxx.2


problems I have:

>From msws1or lx1.., I can ping dns1, it returns192.168.1.200, but from
dns1, when I ping msws1, I hope it will return msws1.mydomain.net and
the ip address. But it can not find the box. So dns1 did not get any
entry from dhcp (linksys) or linksys did not export its lease
information to dns1. When I ping lx1, it returns an ip address outside
of mydomain.net. Because there is a server in the internet have the
same name. That means my dns1 queries ISP's dns and gets that ip
address back. But if I ping lx1 from msws1, I get correct ip address.
I assume this information is returned from linksys, instead from dns1.

Anything I missed? Any suggestion for dns1's named.conf ?

Thanks in advance.

Chang