On your A-side production network, you have your default 0.0.0.0/0 route pointed back to the PPP1 interface. This default route should have a next-hop of your NAT firewall connected out to your ISP.
You should also have a static route to 172.21.1.0/24 with a gateway of 10.10.10.2
On your B-side router all you really need is a default route pointing to 10.10.10.1 on the other end of the PPP link because it's the only link out to both Production and the Internet.
It's best practice generally to reference the other side IP address rather than the interface.
So, you should wind up with something like this as your only static routes:
Destination Mask Next-hop
0.0.0.0 0.0.0.0 [inside IP of firewall - 10.20.5.2 perhaps?]
172.21.1.0 255.255.255.0 10.10.10.2
0.0.0.0 0.0.0.0 10.10.10.1
You will also need to configure your NAT firewall with the 172.21.1.0 network having permission to NAT out to the Internet just as the 10.20.0.0 subnet does. And you'll have to add a static route on the firewall like this so it can get back to the branch office:
172.21.1.0 255.255.255.0 [10.20.X.Y - interface IP of Production router]
Thank you for the information. I was over-thinking the problem and creating bigger problem for myself. I used your input and I now have everything talking and my branch office is now on the internet.
Thank you very much!!!!!!