When driving over 70 MPH the whole car starts to shake?

This is typically a tire balance issue; I would remove the front tires and have them balanced or switch them for the rear tires to see if that makes a difference. Please go over this guide as well:

https://www.2carpros.com/articles/steering-wheel-shakes-when-accelerating-or-braking

If can be the lower ball joints but they should have caught that in the wheel alignment. Please upload videos in your response of any problems so we can see what to help you with.

Hi,

When the alignment was done, all steering and suspension components should have been inspected to confirm there wasn't an issue. So, I will assume that was done unless you tell me otherwise.

When you start to feel the shaking, do you feel it in the steering wheel or the floor/seat of the vehicle more?

If it is in the steering, check the front tires and wheels for damage. If it is in the seat and floor, it is likely from the rear of the vehicle. So, has anyone checked the universal joints on the drive shaft? Do you notice any clunking when shifting into reverse or drive? A faulty or worn joint can cause this to happen.

https://www.2carpros.com/articles/how-u-joints-work

Let me know. Also, let me know if the shop did check the aforementioned components.

Take care,

joe