Have you tried this:
Downloaded your library book to ADE.
Then plug Kobo into PC
ADE should automatically detected Kobo and reauthorized.
Sync to Kobo.
You can also try this:deauthorize Kobo in Adobe Digital Editions (ADE) using Ctrl-Shift-E- deauthorize computer in ADE using Ctrl-Shift-D- remove the My Documents\My Digital Editions folder from computer WARNING: backup your books if you need to. - remove the G:\Digital Editions and G:\.adobe-digital-editions folders from your Kobo (G: is the drive that is usually uses on your computer).- unplug the Kobo- reset the Kobo to factory settings via the Settings->Advanced choice in the Kobo menu.- reinstall ADE, authorize the computer to the new Adobe ID- plugin the Kobo, authorize it to your new Adobe ID
From what I am hearing and seeing the only way to get the file onto your iPad is to get it out of Adobe Digital Editions, so it functions as a normal PDF or EPUB file. So in other words you can not download Adobe to your IPad air because there is no app for it in your App store.You can download adobe on your kobo mini. To do so go to this link: http://www.kobobooks.com/adeBasically it is telling you this:
Connect your Kobo eReader to your computer and select Manage Library.
Start Digital Editions.If you were already using Digital Editions, restart it so that it will find your eReader and start the Device Setup Assistant.
Click Authorize Device.
Click Finished to complete the process.
Basically Adobe can not be installed on your IPad Air but Adobe can be installed on your Kobo mini. IPad Air will only let you install apps from their App store and Adobe is not one of them. You can install Adobe on your Kobo mini itself.Go to this link and click on number 4 and it will tell you how to install: http://www.kobobooks.com/adeBasically here is what it says "
Before you can use Digital Editions to transfer books to your Kobo eReader, you must authorize your eReader with Adobe. When you authorize your Kobo eReader, Adobe adds it to the list of devices associated with your Adobe account. Adobe limits the number of eReaders and computers you can use with their software, which is why this is necessary.
Authorizing takes only a moment.
To authorize your eReader:
Your eReader will now be listed as one of your Bookshelves in Digital Editions. You can drag books from your Digital Editions library to the eReader icon to copy them to your eReader".