Is the tire wearing evenly, or on one edge, or on both edges, or in the center, or cupping, or chipping, or anything else weird?
It's
fine to move a tire from one side to the other.
The issue is something about the tire wearing in for the side it's on, and not riding smoothly when you put it on the other side. It doesn't matter if you switch it from one rim to the other, the reason to dismount it is to flip it and remount it. Nobody does this, everybody just leaves it on the rim and does the regular tire rotation. If move it and find it's not riding smoothly, you can try having it dismounted, flipped, and remounted with what was the inside now on the outside.
http://www.tirerack.com/tires/tirete....jsp?techid=43
Do style A for FWD vehicles. In your case, if you just want to swap the front tires, just do that instead.
Do get the car aligned. If it's pulling that bad, handling may not be safe, and tire wear definitely suffers, and I suspect that fuel economy suffers.