domain name system - How does one configure UFW to allow private DNS requests, but block DNS requests from internet

I have an Ubuntu Server 12.04, with two network cards:

• eth0 is
  connected to the internet


• eth1 is connected to a private
  network (192.168.10.1)
  

The server is configured
as a gateway and hosts DNS and DHCP fro the private network. Computers in the private
network (say with IP address 192.168.10.50) can successfully connect to the internet.

The UFW rules look as
follows:

Status:
            active

To Action From
-- ------ ----
22 ALLOW
            Anywhere
80 ALLOW Anywhere
443 ALLOW Anywhere
67/udp on
            eth1 ALLOW 68/udp
53 ALLOW Anywhere
22 ALLOW Anywhere
            (v6)

80 ALLOW Anywhere (v6)
443 ALLOW Anywhere
            (v6)
67/udp on eth1 ALLOW 68/udp
53 ALLOW Anywhere
            (v6)

Any internet user
can query my DNS server. I'd like to block such requests as it poses a security risk. I
reset the firewall, allowed access to ports 80, 443, 22 and typed the following to only
permit devices on the private network to make DNS
requests.

sudo ufw allow in on
            eth1 to 192.168.10.1 port
            53

When
type the following on a Windows computer (with ip address 192.168.10.50) in the private
network:

nslookup google.com.
            192.168.10.1

I get a
response back that looks as
follows:

DNS request timed
            out.
 timeout was 2 seconds.

Server:
            Unknown
Address:
            192.168.10.1

When I
reset the firewall and allow access to port 53 from anywhere, everything works
again.

sudo ufw allow
            53

How does one
configure UFW on 192.168.10.1 to

• block incoming
  DNS queries from the internet (aka eth0)


• allow computers
  in the private network to make dns queries


• allow the dns
  server on 192.168.10.1 to forward internal DNS requests to the
  internet


• work for both IPv4 and
  IPv6