问：后端敲打/颤动

I have a 2010 GMC Acadia. Last Friday my car didn't feel right. Thought I had a flat because of the fluttering sound in my rear end. Later that morning I Ended up getting a flat and a screw in the other tire (both passenger side.) they plugged the front and replaced the rear pass. No more noise. Fast forward to this Friday night noise is back as is a clunking sound. Took it to get looked at. Suspension is all good. They suggested could be the drivers rear tire is so different in tread depth that it is tricking the speed sensor to fool the rear differential. They suggested I change the rear tire and that should fix it. Asked if I was doing any further damage driving it. They said no. I drove it home yesterday and out today around town. Fluttering is worse and noisier. I'm sure it has something to do with the rear diff from everything I have read. So my question is... Any suggestion of next step? Will tire make that much of a difference? I have owned the car since 88000 and have no record

我的汽车有112000英里。
My car has an automatic transmission.