Electrical?

What is your question?

I have recently changed my car battery. I have had the alternator checked three times and test good as new everywhere i have it checked. The problem i am having is that early in the mornings when i come to a stop light or turn my car off to run into the gas station then come back out to leave my battery seams to get really weak, my lights all dim and it takes a strain when i puch the brake petal