With ours, after blocking the trailer wheels, we jack up the trailer with the hitch jack to relieve the pressure on the 2 round bars, then take them off, along with the hold down pins (they're easy to set down and forget so don't lose them). Once that's done, we lower the trailer back down so the tongue is resting on the hitch, release the ball locking safety device, then jack the tongue back up to free the ball and pull away to get out from under the tongue. We store the round bars and pins in the back storage compartment of the trailer.
If you use the pry bar to free the round bars on the hitch, be very careful! They can be under considerable pressure and when you free them, they come off with some force. if you're in the way, they can really hurt you.
As for the hitch in the receiver on your tow vehicle, we leave our in place with a locking receiver pin. As I' sure you have noticed by now, it's a little on the heavy side and I'm basically lazy and don't want to have to lug it around.