My car makes a deafening rumble sound when I accelerate. I've had my muffler replaced on this car twice before, but this sound is so much louder and comes with the floor vibrating. The sound appears to be coming from right underneath the drive shaft. Other than that, the car seems to be running just fine. What could this be? Should I take it to a muffler shop or a regular garage. It's an old car (1996) but very needed.

There's a flexible part right in the exhaust system at the engine. That part has failed on your car. Call around repair and exhaust shops for estimates. Both types of repair shops should be able to handle the replacement.

Well, you don't have a drive shaft as this is front wheel drive. Being the muffler is at the rear or more toward the rear of the car they shouldn't have had to mess with anything where or in the vicinity of your drivers seat, but they may have removed the hanging brackets that hold the exhaust system up and may have forgotten to re-install the front hanger causing it to vibrate as around the drivers area it is a tight fit and wouldn't take much for the exhaust to touch some part of your car causing a rumbling noise. I isn't to difficult to climb under the car and look around, one thing could be a loose, SHIELD. Catalytic Converter No. 7 in diagram, so look at these parts and you can see in the diagram that a possible loose parts could be your problem, so just use this diagram and start banging around on things and if that's not easily solving the problem, then we would have to look in a different direction.

Bye the way, click on the picture to make it more readable.