Interesting idea. Why exactly would you want to do that though? For extra security on your wallet there are many things to do like encrypting wallet, creating new wallet instance and taking the private keys completely off Internet, etc. I don't think the node #2 (inside the secure net) will be able to transfer/receive anything from the main network without being synced in the first place. True it is getting sync only from node #1 but node #1 does not have any control over what goes on the main network.
Also as a suggestion you might try to see if second node 192.168.1.15 can communicate over the Bitcoin ports to the first node (maybe that is the reason it doesn't connect).
Regards
That's the purpose of a DMZ. Only the node in the DMZ can communicate with the internet and therefore act as normal in receiving and transmitting blocks and transactions. The node on the secure network can only connect to the node in the DMZ. Because it can do that it can transmit and receive everything it needs to and still be completely inaccessible from the internet. I used to design similar security solutions for many other applications (email etc.) before I retired from the IT business.
It's often done with one firewall but is much more secure if you use two similar to this diagram. The node in the DMZ is acting as a proxy server and this a very good way to keep a hot wallet secure.
