Monitor Jenkins node/slave health
To me it looks like you are trying to reinvent the wheel. As I understood you would like to restart a container if a health check fails. As you are using docker you should use a orchestration platform in my opinion like Fargate (ECS) or Kubernetes (k8s). I know from the latter that it is possible to define healthchecks, like readiness and health probes. If the health check fails, kubernetes will restart the POD (auto healing). 

It could be possible that you would argue that k8s is not an option. If that is the case, you could also have a look to AWS OpsWorks. Although I did not try it myself yet, it is able to perform auto healing as well.