AR coated eyeglasses?

I went to America's Best (mistake) and got my eye exam and glasses last Thursday. I got the AR coating and scratchresistent coating on both. I picked them up this past Wednesday. They gave me my glasses and when I got outside into the sun I could see problems. In one pair a lense had two scratches on it and on the other the AR coating had waves in it which has gotten worse since then. I went back in and he finally agreed to send the scratched pair back and when those came back he would send the pair with the waves in the AR coating.

Now it's Sunday and there is a big scratch in the lense with the AR coating problems. It's like the coating seperated because it's not deep at all and mimics one of the waves. I wear them or keep them in a case at all times. With the care and the scratch resistent coating there shouldn't be a scratch.

My question is could the messed up AR coating have messed up the scratch resistent coating on that lense? Could the AR coating be coming off