Brake pedal is stiff and the car pulls left or right when braking (occasionally)?

One day, the left side of the car(wheels) fell into a pothole while I was breaking at least 50%(strength), then the car started pulling to the left every time I was braking. Then I did an emergency brake stop and the problem was solved.
After that it kept coming every time I would go in a pothole while breaking, I had my mechanic to check the car, he checked brake calipers, pads, brake hoses, ABS sensors (through the diagnostic system). I then took the car for wheel alignment and checked the tire pressure at a tire specialist, then my mechanic told me it might be the alignment of the steering wheel IN the ESP Module, so I took the car to Nissan dealership and they checked the car and they told me that they put the car on diagnostic system and the steering wheel was not aligned in the ESP, ABS, ECU.
Then I got the car and they told me if it still happens it means that I need to change the ESP, ABS, ECU.
I got the car, two weeks no issue. Then today, out of nowhere, the problem came back. No pothole, just driving on a very nice road. And my concern is that now not only does the car pull on one side (started pulling to the right, then I did an emergency brake stop and now it pulls to the left), but also the brake pedal becomes very stiff as if the servo is not working. But then it gets soft again (not perfect but a bit softer) and then it is stiff again.
Please help.
Recent changes to the car.
I switched to Hybrid terrain tires (something between all terrain and mud terrain tires) but the problem started before changing the tires.
two years ago I upgraded the suspension to a full 2inches lifting kit specifically made for my car from TJM, I have polyurethane bushes all around and camber correction bushes in the front, the car was aligned perfectly and had no issues whatsoever, I have heavy duty ventilated brake rotors in the front from Milner offroad, and I have replaced both brake cylinder approximately 2 years ago.