My first recommendation would be to separate in your head the Docker development environment from the Docker production environment. They can be very different, and that is OK.

For production you want the Docker image to be built when PRs are merged to master (or whatever your flow is). Google Container Builder makes that very easy, you can set up a trigger to build an image and push it to the registry when there are changes to git (code merged to a branch, tag pushed, etc.). Then you need to automate getting that deployed, hopefully to Kubernetes, but that is a different issue.