You can use a different container as network in docker: 'container:<name>' would route the container traffic through specified container.

Example vpn container:

  docker run --name foo --cap-add=NET_ADMIN ...

Other container:

  docker run --net=container:foo ...

Now you'd need to specify the respective routing rules [1] in the container.

[1] i.e. https://github.com/bubuntux/nordvpn/blob/master/start_vpn.sh...