Connection between two networks with different IPs and identical
That does not match the information in your question. Your two networks have completely separate subnets, but they use the same IP (IPv4).
Routers route packets between networks.
One problem you have is that the devices in Network 1 need to have a gateway configured, otherwise they cannot communicate outside the network. The gateway is a router and the host on the network that knows how to reach other networks. A host will determine if the destination of a packet is on a different network, and it will frame the packet with the LAN address of the gateway for a packet destined to a different network.
It looks like you just need to connect Network 1 to your router and configure that router interface to be in the same network, then configure the hosts on that network to use the address of the router interface as their gateway. The router should automatically route packets between the networks.