Front end shaking and second question passenger electronic door lock

2001 Lexus RX300, wheels are rebalanced and rotated every 5000 miles, when driving the car from start up to freeway speeds the car doesn't shake or rattle, but when you take your foot off the gas and the car slows down once it hits 55 mph it shakes till it gets down to between 50 and 45 mph. I took it to two mechanics and all they did was put it on the computer and said nothing is wrong. Could the motor mounts be bad?

second question: same car the passenger door will not lock or unlock with the power lock or the key.
I checked the (2) fuses that state that they control the windows and they are both OK?