I can relate
When my AH went to jail for 2 years, he had to become sober. Oh, he was so regretful, all of the horrible things he did to me, all came back. He wrote letters and was so sorry. When he got out, 3 days later he was using again and the crazy train took off in its usual direction.
One week of sobriety is nothing. Sorry
If it was one year of sobriety and he wrote you that would mean he thought about it, analyzed and REALIZED what he did. When you are coming off stuff, you become super emotional. Right now he is riding on his emotions, up, down, down, up. Good for you for holding up and standing your ground. You deserve to be happy