When driving I am having trouble keeping my SUV in a straight line

Always "sawing" on the steering wheel to keep it straight. It feels very loose like it's got flat tires. I had my mechanic check it out and he said he could find anything wrong. All he said was it could be "cheap tires". About two years ago I turned onto a road and the passenger side rear wheel went into a hole causing it to bottom out. I wonder if that could gave been the issue and if so what happened? BTW, I have had several front end alignments done and it never corrected the problem.