You using summernote is not a problem.
If you look at my project there is a js library called: languagetool.min.js
This is a modular library for ContentEditable. All you have to do is create a map for summernote of all the functions. You can use the TinyMCE plugin(fully mapped) and the CKEDitor(not fully mapped) as a guideline for making your own plugin.
95% of the work is done in that module, you only have to fill in the last 5%.