2000 Buick Regal Car shakes at 35-45 MPH

I 1st thought it was tires and they looked great so I rotated them. Then I drove car again and figured out it starts shimmyin when I slightly acclerate at mostly 35-45 mph. I checked motor mounts and both lowers was broke. Relaced them and no change. I took it by a shop and they drove it and come back saying maybe the trans, but it was replaced less than 30,000 miles ago. A buddy came by and we drove it, soon as he felt it he said CV joint. We checked the axles and feel some up and down play on both inner CV joints. Is there anyway to make sure both axles need changed or am I missing the real problem?