There are several methods, but bolt the remover to the BB cup. You'll be glad you did. If you can get a fixed wrench that fits you'll be better off if\when you whack it with a hammer. My favorite is a dead blow hammer.
Mounting the removal tool in a vice is an interesting idea. I've done it for freewheels, but never for BBs. You would need lots of room on your work bench to swing the frame around. You would get lots of leverage though.
There is an easy to remember which way to turn a BB cup on either side.
With the wrench pointing down at the ground, move the wrench towards the rear of the bike.