The symptoms are of tire imbalance. Yes, the same has happened with two
sets of front tires - it shouldn't have - but here we are.
Two tire imbalances need to be addressed: static and dynamic.
All tires have heavy spots; some will cause sufficient oscillation to
bounce tires off the roadway at 55 mph!
Dynamic balancing is to offset the tire's outside wall vs. inside wall
imbalance for that oscillation will cause shaking in the steering. This
is what you are feeling.
I've had personal experience of a tire shop's morons "balancing" new
tires on the shop's "electronic machine" that only days later, and at
the same shop, needed 1.5 oz weight corrections! No one batted an eye,
they acted like nothing had happened - business as usual. So don't
Finally, if the problem isn't solved by balancing one should not
overlook the shock absorbers; worn out shocks could be involved, but
first deal with balance.