Yes it is being caused by the towing as the trailer must have been too heavy for your Datsun's wheel suspension. You must always make sure your car can handle the weight of what you are towing. Check the manufacturers manual beforehand.

What does "lost some strength" mean? They aren't holding the car up at normal ride height? That's weak springs. They don't grip in snow like before? That's due to tread wear. How far did you pull the trailer, a mile or cross-country? How heavy was the trailer? I regularly drag around a tandem axle enclosed trailer that's bigger and heavier than the '88 Grand Caravan I pull it with and don't have any problems. An '89 or newer model with the computer-controlled transmission would explode in a pile of sweat before I got to the end of my driveway. It all depends on what you're pulling, what you're pulling it with, and how far.