Re: Is it REALLY asthma?
It may be that your step-daughter has intermittent asthma. Asthma is now classified as either intermittent or persistent (they don't use the word "chronic" any more) and either of these types can be mild, moderate or severe. It is likely that your step-daughter has presented real symptoms in the doctor's office with sufficient frequency to continue to have the meds prescribed for her. Twice a year would be enough for most doctors to do this, for fear her asthma could worsen at any time.
It is possible that something in her mother's environment could be the cause, or even something in school or church or some other environment where she spends time when she is in her mother's care. (Maternal grandparents house, even).
Stress can bring on an asthma attack or worsen one, but normally only in people who are already predisposed to asthma. It can't really cause asthma.