How to make communication between Production network and Isolated Network using Linux machine as a router?

You are using the same subnet on both networks, essentially it's like it being the same network. First change this, for example using 192.168.109.0/255.255.255 as subnet for your testing lab and retry.

Okay, now that you splited in two subnets, another thing i notice is that you have some firewalling rules and some NAT ones that to me at least do not make sense. Try flushing your iptables rules:

iptables -t nat -F
iptables -t nat -X
iptables -t nat -Z

iptables -F
iptables -X
iptables -Z

Then readd only the NAT one:

iptables -t nat -A POSTROUTING -o eth0 -J MASQUERADE

Then try pinging from a machine in the private lan a production one, thing should work.

As both interfaces are on same subnet , just bridge them by using below commands

brctl addbr bridge1

brctl addif bridge1 eth0

brctl addif bridge1 eth1

this should work