What is the cause of this? I have a bad rear and two lower motor mounts so does that mean when I replace them it will go away or could it be something else?

 

I would guess that the shaking is caused by the bad motor mounts. I mean if you only had one bad one, I'd say it's probably unlikely. But with three bad ones, it is likely. Either way they need to be replaced. So replace them, and let us know if that fixes it.