The front of my car shifts back and forth at low speed. At high speed everything is very stable. I have checked the air pressure in the tires. It happens equally on braking and coasting in neutral. Any ideas?

 

love to hear someone who knows what this is mine does ity to. from about 30-40

 

You may have a belt separation in one of the front tires. Have a good tire shop spin the tires and check for run-out.