I think you may be running up against a limitation of the specific camera. Pentax, and I suspect Canon, in some of their products have a menu option to disable requiring focus confirmation before shutter release in autofocus modes, the D3100 doesn't seem to have this according to the manual I downloaded. On page 55 of the manual, all three AF modes state that the shutter can only fire when the camera is able to focus, only manual focus can do otherwise. Normally you would use the AF-L button to lock focus in AF modes which should allow for recomposition and shutter release, but if you've repurposed the button, then this is lost.

I would be surprised if this was a limitation of Nikon in general, so I would have to think that it is specific to the D3100 being an entry level dSLR, it could be seen as "helpful" for the average consumer though irritating for somebody trying to do more than party photos.

So, presuming that there isn't a hidden menu option that I didn't see in the manual and you still want to use the button this way, then one option in AF is to manually select the focus point off the center, targetted to the subject you want to have the focus on. That only works, of course, if that subject falls within the focal point selections. Alternately, you could autofocus on what you want, switch to manual focus, recompose, and then release. This should work, I would think, though a little tedious. The final option I can suggest is to manual focus entirely.

Probably not what you wanted to hear... This is what I determined from the manual, though a D3100 user may have better information than I.