Displaying Section from remote site.

I am trying to use this to display a booking calendar and/or booking form from a remote website.
I have been able to get the whole page to display, but I only want and need the calendar section of the page.
What are the steps to create the shortcode to display only a specific section or area and have it be responsive to mobile browsers.
Screenshot of Calendar
This calendar should open a modal from the host/remote website.
The reason we are doing this is the remote site is managing a property for us, however their website and pages have several other properties displayed that we do not want to promote from within our site. By putting the booking calendar in an iframe we can display accurate availability and allow the proper procedures the managing company has in place