MultiNetting a Fedora Core 4 machine

[Brent]

I have a Fedora Core 4 box that sits on two networks and I need it to 
access both networks at the same time.

One interface (ext_cm, eth1) connects to a cable modem and out to the 
internet. I need this to be the default gateway for the machine, meaning 
any traffic originating from the machine goes out this connection.

The other interface (ext_sh, eth0) sits inside a private network on one 
subnet connected to several other subnets. Also this whole network is 
able to get to the internet through a state wide firewall/NAT. The 
machine has a DNS entry on this firewall so when traffic comes in 
through the firewall it gets routed to this machine.

The problem is that when the machine goes to reply to HTTP requests 
coming in on ext_sh it sends the replies out ext_cm and thus when the 
packets get to the clients they reject them as coming from the wrong host.

I need to know how to get the machine to send replies out the interface 
that the requests come in so that they machine is available via its DNS 
address through the ext_sh network.

It looks something like this:

Net <->cable modem<->FC4 Box<->ext_sh network<->router<->firewall<->net

and I need packets that come in from one side to go back out the same 
side, but instead they are all getting sent out the default gateway 
cable modem.

Anyone have any bright ideas?