How to recharge enchanted weapons with a PS4 controller?

Solution 1:

PS4 controller support on PC is very limited, hence the "quirks" your experiencing. It's most likely the PS4 controller doesn't support the "Back" control in its native format.

For more complete support install DS4Windows which fully emulates the XBox 360 controller using the PS4 controller. The program allows you to view and edit all of the mappings, and you can create "Profiles" which allow for having different mappings for different games. It will also allow you to use the controller wirelessly if your PC has Bluetooth.

I can personally attest to the usefulness of DS4 Windows for the PS4 controller, including for use in Skyrim. The applications predecessor, DS3Windows, was equally good for using the PS3 controller. If you ensure the program boots up with Windows you shouldn't ever have to worry about it again.

Protip: DS4Windows also allows the touch pad on the controller to control the PC mouse, allowing you to control Windows away from your mouse and keyboard (such as playing on a TV).