Nr. 1 is the IP address that is desired and that is set in the command starting the worker node, as shown below.
Nr. 2 is the other IP address I do not want to be part of Rancher at all. The necessary setup for the network traffic is done outside of Rancher. All Rancher needs to do is using the first desired IP address, which is 10.1.1.2 in the below example. It should ignore the other address entirely and it should not show up in any YAMLs or anywhere within Rancher (which it does).
Starting worker node with:
sudo docker run -d --privileged --restart=unless-stopped --net=host \
-v /etc/kubernetes:/etc/kubernetes \
-v /var/run:/var/run rancher/rancher-agent:v2.3.3 \
--server https://10.1.1.1:8443 --address 10.1.1.2 --internal-address 10.1.1.2 \
--token theactualtoken --ca-checksum thcachecksum --worker