Shakes when over 50mph

The first thing I would check is the tires. Do they all have plenty of air? Are they baldind or wearing unevenly? Plenty of tread, even on the insides. Probably the most frequent thing I find when people have this symptom is a tire starting to show cords, or about to blow. It could be many other things, but at least you should be able to check the tires yourself. Let me know how it goes.

Drive slow?

Maybe the weights came off from when they balanced the tires. Possibly you hit a nasty pothole and bent a rim, or messed allignment up.

Have someone follow you on multi lane road test and watch tires to see which 1 is shaking.

That's worth a shot I guess. Try to figure out if it's in the front or back too. Shakes and vibrations can resonate throughout the car and be a little decieving as to where they're coming from, buy you can feel it a lot more in the sterring wheel if it comes from the front.

If you cant feel it in steering wheel it's likely in back? So less dangerous you might say. And less dangerous when not shaking we can assume?

I'm sorry. I can't tell you to drive your car. But a rear shake does make me worry less. Double check the psi (with a guage) in the tires. Make sure the wheels are on tight and there is no play in bearings etc. Where did you have your tires done? If it's a chain, possibly another shop nearby can do a free safety check for you.

What I meant was, for example, last week someone came to me with a Jetta with similar complaint. I put my foot on top of the wheel in question and push and pulled on the tire, I could move it by about a solid inch. Typically, you would have to put it on a jack and grab the wheel at say 9 and 3 o'clock to feel the loose bearings. It was so bad in this case I knew what it was without taking the wheel off. Assuming you don't have the time or ability to jack it up, grab the top of each tire and rock it hard back and forth just to make sure its tight. But aside from that, see if there is a Firestone nearby. I would ask them to double check the balance of the tires because you think the weight came off from the tires you just had put on elsewhere. Make sure they will do it for free, at least try. If there's a serious issue they'll find it for you. They always do.

If not in the steering it will be a rfear end rear tyre problem, if you jack rear one at a tme and spin wheel, you may see or feel a fault in the tyre.