I'm no expert either, but I'll add what I know that might help you move on to the next step.
I'm not sure you can actually stop and start services in the API, particularly a specific layer within the API. I think it's an ArcGIS Server thing.
I have a set of data that gets updated every morning. Because they are part of a map service, I cannot just replace the data, as it will say it's locked or being used. So I have to stop and start the service, but it's the entire service. I do this in a batch job that runs on a schedule. The commands are:
C:\gisdata\tools\BatchServiceTool\arcgisservice <name of server> Framework/OWRD_Large_Dams MapServer stop
C:\gisdata\tools\BatchServiceTool\arcgisservice <name of server> Framework/OWRD_Large_Dams MapServer start
From your API, I would think you could go run this job, as you would a python script or some other script. But I don't know if you would run into problems since the service is open in your application.
Good luck.
Dorothy