Just to make sure I'm understanding, you want to run docker containers on demand (and programmatically), but you want to run them on a single machine, so Kubernetes feels like overkill, right?
Your best bet might just be invoking the docker command-line tool directly from your code.
Possibly I'm not the right audience, but a guide on how to get your current docker setup incorporated into your service might be useful for people wanting to give it a spin.