Reading the replies from @doug and @b3n, I've managed to implement the fix by giving a change to the report when the controller is connected.
[48361.273580] usb 1-2.4: USB disconnect, device number 25
[48366.681972] usb 1-2.4: new full-speed USB device number 26 using xhci_hcd
[48366.883070] usb 1-2.4: New USB device found, idVendor=054c, idProduct=0268, bcdDevice= 0.01
[48366.883092] usb 1-2.4: New USB device strings: Mfr=0, Product=2, SerialNumber=0
[48366.883102] usb 1-2.4: Product: PS3 Controller
[48366.890323] usbhid 1-2.4:1.0: can't add hid device: -32
[48366.890366] usbhid: probe of 1-2.4:1.0 failed with error -32
[48366.905149] usb 1-2.4: USB disconnect, device number 26
[48367.449946] usb 1-2.4: new full-speed USB device number 27 using xhci_hcd
[48367.643118] usb 1-2.4: New USB device found, idVendor=054c, idProduct=0268, bcdDevice= 5.72
[48367.643141] usb 1-2.4: New USB device strings: Mfr=0, Product=2, SerialNumber=0
[48367.643150] usb 1-2.4: Product: PS3 Controller
[48367.654388] input: PS3 Controller Motion Sensors as /devices/pci0000:00/0000:00:14.0/usb1/1-2/1-2.4/1-2.4:1.0/0003:054C:0268.0014/input/input47
[48367.706730] input: PS3 Controller as /devices/pci0000:00/0000:00:14.0/usb1/1-2/1-2.4/1-2.4:1.0/0003:054C:0268.0014/input/input46
[48367.707515] sony 0003:054C:0268.0014: input,hiddev98,hidraw6: USB HID v81.11 Joystick [PS3 Controller] on usb-0000:00:14.0-2.4/input0
Good: The driver works even with the latest driver available. It just change the report of the given controller, so, other controllers will remain functional.
Bad: The controller only works with the cable and the player's count LEDs turn on in a weird way.
TODO: I still want to make this driver actually doable. Any help will be very welcome.
GitHub: https://github.com/KanuX-14/GeneriKit
Edit: The original driver will be kept. It can be enabled again by deleting the line 'blacklist hid-sony' in /etc/modprobe.d/generikit.conf.