Bicycle Mechanics - Rim offset from hub?

In order to have spares and to make changing cassettes a snap, I bought a second set of wheels - same as the first. But of course it's never that simple. When I swap the rear wheel the rim in relation to the brakes is offset a bit to one side and I have to adjust the brakes to get them square again. It's not bad - maybe 1/8 to 3/16" difference. (Front is pretty square.)

Other than the annoyance factor, is this an issue? What would I have to do to even them up?

The ideal thing to do would be to adjust the dish on one or both wheels to make them exactly the same. Then you'll never have to mess with it again.

It's brain surgery. First, figure out which wheel you think is closest to right. Put that wheel in your bike and adjust your brakes to fit. Now put the other wheel in the bike. Tighten all of the spokes on one side about 1/8 turn and loosen all of the spokes on the other side 1/8 turn. Repeat until the rim is centered between the brake pads.

Actually you need to see which wheel is properly dished first and then adjust the other using the method above. Ideal is to take to a shop and have them check dish (5 sec job), 2nd choice put into a truing stand, adjust the pointers within about 1/4" from the rim and then reverse the wheel. If it shifts it is not dished properly. If it sits in the same spot left to right it's properly dished.

So the rim should be centered with respect to the faces of the axle locknuts?

I don't have a truing stand, but I could figure out a way to use the frame. Hmmm... The hanger alignment tool might be just the ticket. It would get the dérailleur out of the way so I could flip the wheel, too.

Actually I forgot the third option. Take the wheel off, unship the chain from the chainwheels so there's plenty of slack and you should be able to put in the wheel both ways without interference from the chain. Then just compare the position to the brake pads.