Suzuki: 1998 Suzuki Esteem GL 1.6 ltr. engine, fuel injector cleaner, cv joints

Question
About ten minutes into driving, shaking/vibration begins in steering column around 35 mph and is felt throughout car. Try to accelerate and shaking/shuddering increases. Feels like tires are really out of balance or going flat. Drive another ten minutes, backing off speed a bit, and problem disappears. Can then go 55 mph, or even hit passing gear and car runs smoothly. Changed fuel filter on firewall and some dirty fuel dripped out from old one. Added fuel injector cleaner. Checked for front wheel shimmy. None. Rotated tires. Engine seems to run smoothly when in neutral and has plenty of pep! My daughter, who drives this car, was notorious for letting gas run empty. Someone suggested blowing fuel lines out with air or even changing fuel filter, again. Is there more than one? Have you ever heard of this problem? My daughter is afraid of driving the car and possible break-down.

Answer
Does the vehicle buck and jerk as if you were turning the key on and off rapidly?
If not, it's possible that the CV joints(axle drive joints similar in function to a u-joint) are "dry" or the boot is ruptured as far as having sufficient lubricant in them.  I ran across that a couple of times, and it did not make sense until I had solved the first one.