What you want to do will require a speedy wireless transfer rate. It might be possible if you use small video frames, and slow frame rate.
Even if you used ethernet, the rate would likely not be fast enough to handle tv quality video.
As for the computer, these are being made fast enough to handle the required video rates.
Would you need to dedicate a computer to accepting 3 video feeds and joining them into one? Most likely. You also might need to obtain a special PCI card that has 3 video inputs. (PCI or its sister formats as specified by the computer slot dimensions.)
Don't know what program will combine multiple live videostreams into one.
You may achieve what you want if you draw on a variety of computer functions. There's (1) the USB webcam type of setup, and (2) the incoming ethernet setup, and (3) the incoming from video camera to PCI video card setup.