Trouble Hooking Up Trailer due to "Gear Slack"????

The parking brake should definitely prevent the truck from moving. If it's not then either some component of the parking brake system has failed or the parking brake needs to be adjusted. Adjusting the parking brakes is normally a fairly easy process.

I would check this out sooner than later. Without a working parking brake, you're relying on the parking pawl hold the vehicle in place. That's not what it's designed for and will eventually cause it to fail. This is particularly bad when on inclines. When it does fail, essentially you'll won't have anything holding the truck and trailer in place.