Afraid you've been smitten by the S4 Active hex. This phone has go to be the biggest mistake Samsung has ever made and if I knew the limitations this phone has I'd have never gotten it. I'd gladly trade it in for the standard S4 if I had the opportunity.
To your problem . .. . . . . . . . seems the S4 active and version 4.4.1 and 4.4.2 do not get along very well. We can't root the phone to get some other ROM to work around the problem so the only solution is to find an app that helps you trick the system.
I've found two apps that have given me a great deal of relief as far as moving apps and data to the external SD card. The first is called "CLEAN DROID". Once you install and start it there is an option to unlock or free the SD card to accept moving apps to it and free up your storage on your internal SD. The second is called "ES FILE EXPLORER" . . . . using the USB cord that came with your phone, which allows data transfer and not just charging capabilities found with after market cords, you can transfer files/data from your phone to your PC and back. It opens your external SD card for file/data transfer and I've got my music and pictures stored on the external card as well as lots of game data.
I don't know how it all works in the grand scheme of things but with this software version, which we will never get an update for by the way, and this crappy phone with it's limitations, these two apps have made it tolerable to own the S4 active.