Is the BB stiff, as in "brand new and stiff", or is it "old, broken, and stiff"?
If it's brand new, I'd say give it time to break in before you decide to remove it.
I also find it kind of implausible that you would be able to break loose ALL of the right side threads at once! There must be something else wrong.
Given that it's an aluminum frame, I'd say your chances of causing a lot more damage to the bottom bracket shell are pretty high if you try to whack your bottom bracket out with a hammer. If it were a steel frame, I'd say go ahead and try a hammer as long as you accept that you might damage your already messed up frame some more.