How to autofocus a Canon T3i Rebel with AmazonBasics remote control?
I could be wrong, but my understanding of the AmazonBasics Wireless Remote Control is that it is only for remotely controlling the shutter (i.e., it only works for pictures). In photo mode, it will autofocus after you press the button. One thing to test would be to try enabling autofocus on your camera/lens, starting recording, and stand in front of the camera. Use the shutter to remotely take a picture (the T3i can take pictures while recording). After that, your autofocus should be set. 

Once again, not 100% sure that this would work, but that is what I would try first.