If the front portion of vehicle is shaking badly, it could mean something is wrong with the wheel bearings. Were they checked for excessive play? Your symptom is similar to what is termed as "Death Wobble" and there could be some faults withe the steering linkages. You mentioned the brakes were fine, but if the calipers pins are seized, it could cause the brakes to self apply when heat builds up. This can also result in the shaking.
After getting up to speed, try shifting to neutral and test if vehicle slows down quickly as if the brakes are applied.
Let us know how it goes.
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Monday, March 5th, 2018 AT 7:49 AM