You have to enable TraShadow for the materials recieving the Light after it is passed through the transparent object. This is a raytracing effect and only works for ray traced shadows (yep, it’s not light, it’s shadows).
The other effect you are referring to is called caustics. You can get a build with Fake Caustics here:
You can render the caustics with that build and composite the result into the scene with the nodes compositor or the VSE. If you’re making animations SSS will more than likely add more time to the render than you’re willing to spend.