If Gawyn won't trust the woman he loves and his sister that Rand wasn't involved with Morgase's "death" at all (also his old tutor Bryne already indicated that), but that the Shadow was behind it, it's not tragic, it's simply unbelievable stupid writing. This is especially true, since Gawyn would plot to kill the only person who might save the world in the advent of TG, and thus would actually know that he will become responsible for the deaths of Egwene, Elayne and all other people on the world, just to avenge Morgase's death. That makes no sense.

Besides that, both women could even force Gawyn not to harm Rand, Egwene as his AS and Elayne as his Queen.