extreme shaking over 60 mph

I noticed my 4runner shaking quite badly when I accelerated over 60 MPH in about Nov/Dec 2016 and I didn't DARE put the brakes because it almost shook me off the road. I took it in to Toyota and was told that they could not get the problem to occur again but maybe if I changed the brakes it could get better and I told them to let me go for a ride with them and show them but they said that wasn't allowed so I had to take my 4 runner and basically think I was "Going Crazy". I don't drive my 4 runner too often because I have a work vehicle but I have now started driving it more frequently since taking my children to and from sports. I noticed again a couple of months ago and once again took it to Toyota and was AGAIN there was nothing wrong but that they could go ahead and change my brake pads and turn the rotors for over $800. The weird thing is that my other Toyota 4 runner (2011) had the EXACT same problem. I'm beginning to think think that this is a 4runner problem and not the 4 runner operator problem. I hope others read this and maybe someone else out there has experienced this same problem. I am now heading to a brake shop to get a 2nd opinion on my brake pads and rotors.