New bike wheels dont sit in dropouts perfectly, are washers safe to use?
could it simply be that the new rim is a few millimeters wider and the brakes are making contact because of that? If the wheel is seated into the dropout all the way, the quick release will have enough force to fully clamp the frame to the hub securely. Check by unclamping the qr, putting some body weight on the saddle with a shoulder and reclamp the qr. Beyond that, mattnz's suggestion above is possible. The whole hub assembly/bearings might be too tight or too loose, which is an easy fix.