I have a 2008 Ford Taurus x 3.5 I change the spark plugs coils fuel injectors O2 sensors the oxygen sensor every time it reaches 40 to 50 miles an hour it shakes I put new brakes and rotors new tires in the motor still has a vibration into it when it’s parked
from what you wrote it looks like you have 2 problems. a shake when you hit 40-50 mph and a rough idle when in park. assuming you had the rims balanced when you put on the new tires, i would look at a bad or worn suspension or steering parts. as far as the rough idle it could be a vacuum leak.