Hi Adam, The responsive banner module doesn't load additional jquery, it uses default joomla jquery file. But sometimes other extensions (module and template) still uses their own way to load jquery, maybe because they didn't update their code to fully support joomla 3 or maybe because other reason.
JQuery solves that problem. It will unload all jquery calls from all extensions and then load only one jquery in the proper place.
How can I stop the module from loading jquery and jquery ui?
Umm I don't really understand this, responsive banner slider doesn't load jquery UI. Any reason why did you you think like that?