How can I redeploy a docker-compose stack with terraform?

Terraform has a Docker provider, and if you wanted to use Terraform to manage your container stack, that's probably the right tool. But, using it requires essentially translating your Compose file into Terraform syntax.

I'm a little more used to a split where you use Terraform to manage infrastructure – set up EC2 instances and their network setup, for example – but use another tool like Ansible, Chef, or Salt Stack to actually run software on them. Then to update the software (Docker containers) you'd update your configuration management tool's settings to say which version (Docker image tag) you want, and then re-run that.

One trick that may help is to use the null resource which will let you "reprovision the resource" whenever the image ID changes:

resource "null_resource" "docker_compose" {
  triggers = {
    image_id = "${var.image_id}"
  }
  provisioner "remote_exec" {
    ...
  }
}

If you wanted to go down the all-Terraform route, in theory you could write a Terraform configuration like

provider "docker" {
  host = "ssh://root@${google_compute_address.training-address.address}"
  # (where do its credentials come from?)
}

resource "docker_image" "myapp" {
  name = "myapp:${var.image_id}"
}

resource "docker_container" "myapp" {
  name = "myapp"
  image = "${docker_image.myapp.latest}"
}

but you'd have to translate your entire Docker Compose configuration to this syntax, and set it up so that there's an option for developers to run it locally, and replicate Compose features like the default network, and so on. I don't feel like this is generally done in practice.