Thank you! Your diagram does not match mine, and now I perceive the root cause of the communication difficulty between the webserver and your "insider" network. They are both using the same /22 IP subnet, but the /22 subnet is not a single network. Instead, the subnet contains two separate Ethernet networks.
This is a network configuration error.
There are three solutions.
- Map the two separate Ethernet networks so that each has its own, distinct IP subnet. This only requires the authority to revise the network configuration of both gateways, and any DHCP servers used in your environment.
- Bridge the two Ethernet networks together into a single network. This requires additional network interfaces on the gateways, and the authority to revise the network configuration of both gateways.
- Use a single gateway. Of course, this must be permitted by the administrative or regulatory authority that deploys the webserver.
Edited to add:
Solution 1 can be implemented without any hardware changes, as it only requires changes to IP addressing and IP routing. It could therefore permit an immediate operational solution while you determine your best long-term solution.
Solution 2 will require IP routing governance in order to avoid inadvertent and unnecessary use of the bridge when routing traffic to and from the Internet. The clients should be assigned a default route that does not use the bridge. Additionally, if there are two DHCP servers they will need to be synchronized.
Solution 3 could be as simple as a gateway router with two interfaces. The external interface would have two IP addresses -- a primary and an alias address.
Please let me know if you need any additional guidance.