Send joystick input from one PC to another?

I'll start with the equipment:

• 1 PC (Windows 7) and 1 notebook (Windows 10)
• An original PS2 controller with USB adapter

What's the problem?: The PC doesn't recognize the PS2 with the USB; tried 3 different usb ports and none works. A SNES controller for PC (the cable ends with an usb) works fine. And mouse/keyboard works fine, too. The only problem is the PS2 controller.

The PS2 controller to usb works fine in my notebook, and also in the PS2 (without the usb adapter, of course).
Why do I insist on using it on the PC? Well, for the simple reason that it's more potent than the notebook.
Yes, this could be solved with reinstalling some drivers, cleaning files on the PC, buying a joystick controller with usb, etc But I'm searching for another option.

As the title says, I connect the PS2 controller to my notebook, is there a way to send the signal to the PC? We have wi-fi (3mb). I know of TeamViewer, but I don't think it would help if it's used to games and for the slow connection. I want to believe that there's something that can be shared by bluetooth to just send the input signal of the joystick.

Thanks!