Car pulls right and left when I push the gas and let off the gas

That is a tough one. There are a few things that can cause the pull, but the differential is a different issue. I need you to check 4 different parts on the vehicle. On the rear axle, there is what is called a suspension bar. There are two, one in each side. See pic 1 (highlighted). Make sure nothing is broken, rusted, the rubber mounts are in good condition and look for anything that stands out. If you see something, take a pic and upload it for me to see. I highlighted the parts I'm referring to. However, I didn't highlight the upper suspension arm (number 2 in the pic). Check it as well.

Next, on the front there are tracking arms. See pic 2 (highlighted). Do the same with them. It isn't uncommon for the bushings to go bad and egg shape the steel arms.

Do this and let me know what you find.

Joe