When he reached puberty his asthma disappeared. It is astounding to me that I have lived nearly five decades, known hundreds, if not thousands of people from all walks of life and have only known one person who had asthma. I'm willing to concede that there may be environmental factors other than smoking that are responsible but my gut feeling is that anti-tobacco propaganda, as well as widespread health hysteria are the culprits. Countries in Western Europe where the standard of living, as well as the physical environment, are almost identical to what we enjoy here are not afflicted with anti-tobacco campaigns and do not have the asthma rates we have in the United States and Canada even though smoking rates are a bit higher. Although your concerns about your step-son are legitimate, your theory as to the cause of his asthma is not.
Children are adept at playing one parent off another.
He may be distressed by having to return to your home which is manifested by an asthma attack. He may not enjoy his stay with his mother and wants to make sure he isn't sent there again, reinforcing his desire by an attack. There may be something in his mother's house, other than tobacco, that is triggering his attack. Life is complicated but the understandable desire to find a politically correct villain doesn't obviate the complexity of factors that may be involved. You don't know why these attacks occur and have offered no proof to back up your theory that his mother is to blame.