How do I connect a PS4 controller connected to an Arduino that's connected to a laptop to another Arduino?
this is possible, but the processig bridge can add a lot of delay if not correctly handled, also wifi has a low range, almost 100m by default hardware.

zigbee module has better range (xbee pro are up to 1km) and are microcontroller friendly, you use the as you are using a serial, they will hide their complexity once you set them up, and this can be done by PC.

That mens less code, that mena less error and more ram/flash/cpu so you can do a smarter robot :)

zigbee use the serial protocol to communicate, exactly as you do with the pc. Also arduino can use, with the library SoftSerial, any pin as Serial. So you can keep the HardwareSerial to communicate with pc, and any 2 free pin to communicate with the xbee. So you can use the arduino stand alone, only with the controller, and when needed connect the pc. Then arduino can act as a bridge between xbee and pc, so pc can excange data with the rover. But even without pc your project will be fun.
The same apply for bluetoot or 400/800mhz rxtx module, but not for wifi shield