Why do rear tires look like the woobly tires on an old VW van going down the road? They really frightened my wife on my initial journey.

 

Looks like it's time to get a manual.

 

You will also need a Special Pin Wrench, a Dial Indicator with a Magnetic Base and an Old Brake Rotor that you do not mind beating on (or make a set up you can use a Slide hammer on) so you can get the Wheel Hub off.
And in the process of removing the Wheel Hub it almost always damages the Bearings.

You will see this when you read the Manual.

Resist the temptation to beat the Hub out with a Punch because the area on the shaft there is rather thin and has been know to distort. A new hub is over $250 and as you will see when you are removing yours removing one at the Junk Yard can be a lot of work.

 

Does the special pin wrench have a mercedes part number?

 

If you do an eBay search: Pin wrench socket -axle shaft flange Tool for Mercedes; that will take you to the ZDMAK tool ad. That ad has the Mercedes part number.
It looks like that total cost will be about $48 from them.

There is also another company that sells on eBay; El Paso Tool that sells them.

Just make sure it is for a 123.
Harbor Freight sells inexpensive Dial Indicators and Magnetic Bases. However, the present Dial Indicatory they sell is not in mm so you will have to convert the inch reading to mm.

I have been thinking your problem over. I would jack up the Rear and Remove the Wheel and see if you can feel any in and out or side to side pay when you yank on the Rear Wheel Hub. If you already have the Dial Indicator you could check the play with that.

The above is to verify that it is actually the Wheel Bearings. The reason I mention this is because your Rear Trailing Arm Pivots on Rubber Bushings that sometimes rot out. You do not want to repalce Wheel Bearings if it is the Bushings that are no good.

Also take a look at your Springs.