The other issue, more rare, is that the reader module is not loading in IE.
My problem was that IE11 was not automatically loading the PDF Reader module even though I had it enabled so I had to start by finding the Class ID of the add-on. You can find that by going to Tools, Manage Add-Ons, selecting the offending add-on (you might have to use the "Show All Add-ons" to see it), right click it, then choose More Information. That pulls up a window where you can see the Class ID. For my add-on the value was:
{CA8A9780-280D-11CF-A24D-44553540000}
You cannot copy and paste from that screen to the clipboard so you will need to carefully write down the Class ID. You will need an old-school analog input device like a pencil for that step (I know, so 20th century 
).
Next, go to the registry and find this entry:
HKEY_CURRENT_USER\Software\Microsoft\Windows\CurrentVersion\Ext\Settings\
and see if there is an add-on listed under Settings with a matching Class ID. I did not have a matching key so I needed to create one.
I added the missing key under Settings and then created a new DWORD value under that key. The DWORD is named "Flags" and needs a numeric value of 1 to enable the add-on or 0 to disable it. I wanted to use the add-on so I put in a value of 1.
The combination of these two tweaks fixed my issue. I am not sure if the step above is strictly needed because I initially screwed up and installed the TabProcGrowth key as DWORD instead of String Value. When I changed the value to correct type, I left the earlier step untouched cause if it ain't broken then don't fix it. I also did a master reset of IE under Internet Options, Advanced. That disables all the add-ons (as well as some other personal customizations) so you have to redo those changes as well.
Mine was a clean install on a brand new, out of the box HDD following the untimely death of my old hard disk (RIP) so your mileage may vary if other apps have been messing with the registry. I managed this with Win 7 Pro X64 and Adobe Acrobat Pro 11.7.