How about hooking up your "Next" and "Prev" buttons to the plugin's scrollTo method? From the documentation link you provided, it looks like you can scroll to an element given an ID (requires each element have an id rather than scrolling using element index) for some reason:

var elID="#el-1"; $(".content").mCustomScrollbar("scrollTo",elID);

There isn't a lot of support for getting the current item in the scroller, so you'll probably have to manage that yourself (through an index that can be updated either through scrolling or clicking the next/prev buttons) and use the method above to scroll to the next div.

I've made a fiddle for this using a regular scroller (not with the plugin). Here's javascript source of it: