Is it possible to connect my DS4 controller to both my computer and PlayStation?

Solution 1:

Ross' comment is correct. In the same sense that your phone can't be connected to two Bluetooth speakers at once, the same goes for the controllers. At least in the Windows world, I am able to connect my controller to my computer via a USB cable, while still retaining the Bluetooth connection to the PS4 itself. While I can't say the same for a Mac, I would imagine that it applies as well.

Of course, this is a non-wireless solution, and can restrict how far away you'd like to be from your Mac. If anything, Christmas is coming up, and if you celebrate it, it may be a good time to ask for a second controller if you'd really like to stay wireless.