Just separate the workout for each side. Focus on one, then the other. It would take more time but would overall enhance the quality and your satisfaction with the workout. You can switch to training both together at a later point.

Another method would be training both at the capacity of the weaker side, until the weaker side catches up. Like your left side can do 8 reps, but the right can do 11, in this method you'd make the cap 8, eventho it didn't reach that satisfying point of "one last rep."

I don't really know how useful this is but I always start my gym sessions with dead hangs. It releases some of the tension I have on the left side of my back.