Shaking after ignition, goes away after acceleration

Once or twice a week, the front of the car will start vibrating and shaking right after ignition. It goes away after driving a short distance. I also have the same rough idling where I have to turn off all AC or air vents when idling, otherwise my car struggles and shakes. The radio display also turns off randomly, but the radio still works. I was thinking engine mounts, but maybe electrical problems. Please help!