If you even got the wheel to move, it's <1mm, not 2-3mm. Figure out the actual interference. Also, do you have brand new brake pads? With a sliding caliper, caliper-spoke clearance changes with the brake pad thickness.
If it's really <1mm of interference and your pads are new, you can shave the caliper or grind down the brake pads with a belt sander. If your pads aren't new, you've got even bigger problems and should get wheels that fit.