Okay, let's see if these pauses are enough to get this passing

test/integration/roles/test_docker/tasks/docker-tests.yml

@@ -8,6 +8,7 @@
     image: busybox
     state: present
     pull: missing
+    docker_api_version: "1.14"
 
 - name: Run a small script in busybox
   docker:
@@ -16,6 +17,7 @@
     pull: always
     command: "nc -l -p 2000 -e xargs -n1 echo hello"
     detach: True
+    docker_api_version: "1.14"
 
 - name: Get the docker container id
   shell: "docker ps | grep busybox | awk '{ print $1 }'"
@@ -25,6 +27,10 @@
   shell: "docker inspect {{ container_id.stdout_lines[0] }} | grep IPAddress | awk -F '\"' '{ print $4 }'"
   register: container_ip
 
+- name: Pause a few moments because docker is not reliable
+  pause:
+    seconds: 40
+
 - name: Try to access the server
   shell: "echo 'world' | nc {{ container_ip.stdout_lines[0] }} 2000"
   register: docker_output
@@ -43,6 +49,7 @@
       TEST: hello
     command: '/bin/sh -c "nc -l -p 2000 -e xargs -n1 echo $TEST"'
     detach: True
+    docker_api_version: "1.14"
 
 - name: Get the docker container id
   shell: "docker ps | grep busybox | awk '{ print $1 }'"
@@ -52,6 +59,10 @@
   shell: "docker inspect {{ container_id.stdout_lines[0] }} | grep IPAddress | awk -F '\"' '{ print $4 }'"
   register: container_ip
 
+- name: Pause a few moments because docker is not reliable
+  pause:
+    seconds: 40
+
 - name: Try to access the server
   shell: "echo 'world' | nc {{ container_ip.stdout_lines[0] }} 2000"
   register: docker_output
@@ -62,5 +73,4 @@
       - "'hello world' in docker_output.stdout_lines"
 
 - name: Remove the busybox image from the local docker
-  shell: "docker rmi -f busybox"
-
+  shell: "docker rmi -f $(docker images -q)"