I have a similar issue. I do see the Adobe Acrobat SharePoint OpenDocuments Component in the All Add-ons, but when I try to click on a PDF document in SharePoint 2010 using IE11, it tries to open it in Acrobat DC, but gets the following error:
"There was an error opening this document. The filename, directory name, or volume label syntax is incorrect."
I can click open in new window or tab, and it opens in the browser, but it won't open in Acrobat DC. I can download the document, and it opens fine from my computer, but not from SharePoint 2010. I can also open Acrobat DC, click File > Open, and open a document from SharePoint and that works fine as well.