1993 Chevy Blazer car jerking while stopped

1993 Chevy Blazer V8 Four Wheel Drive Automatic

my car has been jerking when the car is stopped in either neutral, drive, or park. It also does it a little while the car is in motion if the car stays around a constant speed like if the cruise control is on. It does not jerk when the car is accelerating. I also found that I tends to not do it as bad when the ac is turned off. We just had a new engine installed about a month ago but I dont know if I wore the engine in good enough because I drove the vehicle from arizona to colorado staying around 65 mph and back from colorado to arizona going well over that speed. What might be the problem? Is it engine or something else like transmision? Also my car also has a relatively low battery power staying around 12 lately. Is there any way that the alternator might have something to do with it?