Containers in different networks can not communicate with each other because iptables drop such packets. This is shown in the DOCKER-ISOLATION-STAGE-1 and DOCKER-ISOLATION-STAGE-2 chains in the filter table.
sudo iptables -t filter -vL
Rules can be added to DOCKER-USER chain to allow communication between different networks. In the above scenario, the following commands will allow ANY container in mynetwork1 to communicate with ANY containers in mynetwork2.
The bridge interface names of the network (mynetwork1 and mynetwork2) need to be found first. Their names are usually look like br-07d0d51191df or br-85f51d1cfbf6 and they can be found using command "ifconfig" or "ip link show". Since there are multiple bridge interfaces, to identify the correct ones for the networks of interest, the inet address of the bridge interface (shown in ifconfig) should match the subnet address shown in command 'docker network inspect mynetwork1'
sudo iptables -I DOCKER-USER -i br-########1 -o br-########2 -j ACCEPT
sudo iptables -I DOCKER-USER -i br-########2 -o br-########1 -j ACCEPT
The rules can be fine tuned to allow only communications between specific IPs. E.g,
sudo iptables -I DOCKER-USER -i br-########1 -o br-########2 -s 172.17.0.2 -d 172.19.0.2 -j ACCEPT
sudo iptables -I DOCKER-USER -i br-########2 -o br-########1 -s 172.19.0.2 -d 172.17.0.2 -j ACCEPT