Migrating between hosts on internal IP

I have a Proxmox host that has two physical Ethernet ports. eth0 is the public network,. The internal network is connected to a 1GB VLAN.

eth0 is configured with a public IP - e.g. a.b.c.10 and eth1 is configured with an internal IP 192.168.0.10

I recently added a second host to the cluster with a public IP a.b.c.11 and internal IP 192.168.0.11
However when adding this host I added it using the public IP. So when I migrate a VM between the two hosts, it uses the public IP not the internal IPs.

I do have /etc/hosts configured on each server e.g.

192.168.0.10 vmhost1
192.168.0.11 vmhost2

Is there a way to force internal traffic across eth1? Or, should I remove the second node from the cluster and add it again using the internal IP?