MyBinder sessions have a terminal you can access. Example with a few terminals opening can be accessed by going here and pressing ‘launch binder’ below the file listed. (Not what you need, but shows possible to go right to window with terminal using workspaces.) Could you get what you need just triggering launches of sessions from Wordpress site with URL? Study the URLs of the launch binder badges to get an idea of the pattern and get help making them at MyBinder.org.
There is also Juniper and Thebe.
Also here, see: