2003 Cadillac Deville my car shakes

I can feel my car shaking under the seats when I'm accelerating at aroun 45 to 50 mph. I stops at around 55mph. It also stops when I let off the accelerator. If no one is in the passenger seat it does not do it. It also does it again at 70mph just not as bad. My tires are fairly new and I've have them rotated and balanced twice but it didn't correct the problem. My dad is a mechanic and he's never encountered a promblem like this before. It's really got him scratching his head. Any ideas for him to Check would be of great help. Thanks!