Embedded Shiny App - Interactivity with wider DOM

[Jeremy Gofman]

I'm interested in embedding a shiny app in a web application. Shiny is a miraculously interactive environment but there does not seem to be much functionality in the way of influencing inputs based on clicks in the DOM outside the immediate scope of the shiny app. 

Currently, I have the shiny app running locally, as is the wider webpage. The shiny app is embedded via an iframe.

Is there a way to map my own html buttons to their corresponding inputs in the shiny ui?

Reading online, there is a lot in the way of implementing JS and JQuery within the shiny app in its local directory, but I'm looking for a way to have shiny listen for inputs from the webpage in which is it embedded. 

Any ideas?

-Jeremy