Sounds like you're over steering when backing up. Try laying down a 2X2 or a chalkline beside the trailer tire going into the garage. Using your driver's side mirror always stay close to that line only making small corrections. Check your passenger side mirror often so you don't back into something. When I taught my son to back up we went to a mall parking lot after hours and used the stall lines as a guide. If all else fails you can always put a hitch on the front of your tow vehicle. It'll become easier with time. Can't help you with the switch on your trailer as I've never seen one.