With some bikes the wheel is not self-centering. This is especially true on less expensive bikes with a separate derailer hanger vs one that is integrated into the frame. If you look you can see that the left and right dropouts are not symmetrical.
In such cases you must manually center the wheel when you remount it. The best way to do this is to install the wheel, place the bike on the ground with the quick-release loose, hook your hand under the rim near the brakes, and move the rim left-right until the wheel is centered between the brakes. Then, while holding the rim, tighten the QR. If the brakes do not self-center well enough to serve as a reference point you may need to sight between the tire and the two seat stays (rods from seat to rear hub) to center the wheel.
If, on the other hand, you have a bike that should be self-centering then either the axle is not all the way seated in the dropouts or you've somehow messed things up while installing the hitch. Did the installation require disassembling the quick release?
The rubbing you describe is a sign of a misaligned wheel. No wheel is perfect, but if its enough for you to notice the wheel probably should be aligned in a bike shop. (If you recently bought the bike the shop should give you a "touch up" alignment for free.)