Just curious, were the two new tires the same make and model as the other two tires? When I put two new tires (same size as the OEM tires, 155/80-13) on my wife’s 86 Dodge Colt, the car vibrated badly over 50 mph. The size was correct, but the tires were from a different manufacturer than the OEM tires. Upon visual inspection the new tires appeared larger than the OEM tires and the size difference was enough to give the car the shakes. I replaced the tires with four new Bridgestones and the car was fine after that. I’m guessing that actual tire size may vary from manufacturer to manufacturer.
On the other hand, when we bought a 98 Windstar, it came with 3 Goodyear Invictas and 1 Regatta (215/70-R15). Eventually one of the Invictas slipped a belt and I had to replace it with a Goodyear Integrity (closest I could find). Three different tires, but from the same manufacturer. I had no problems during the four years I drove it this way.
Ed B.