The 2003 has 'open' differentials, so yes the wheels will spin if one side or the other has traction. (As opposed to EITHER front or rear)
First, assure that the propshaft hasn't been removed by a previous owner. (Expensive to replace if the u-joints were causing vibrations)
If that is OK, have the shop replace the rear differential fluid with genuine Honda Dual Pump Fluid. You need the specific friction characteristics for the pumps in the rear to work as designed.
Post back with the outcome.
First, assure that the propshaft hasn't been removed by a previous owner. (Expensive to replace if the u-joints were causing vibrations)
If that is OK, have the shop replace the rear differential fluid with genuine Honda Dual Pump Fluid. You need the specific friction characteristics for the pumps in the rear to work as designed.
Post back with the outcome.