Motor mounts can contribute to a DW situation, but normally will not cause it. Anything that can store and then release energy can add to the problem, including motor mounts. First things first. Did it ever drive OK with this exact suspension configuration? If so, then something either wore out or got loose.
The easiest way to diagnose things is to get a helper to get inside and rock the wheel back and forth. Look closesly at each and every joint. Look for slop, allowing movement. It is possible that the caster is off, and that good shocks and stabilizers were hiding the problem, but not normally.