First, a danger sign: no or poor weight gain over the last 1.5yrs means that she has chronic illnesses, & chronic illness will cause poor appetite (but being hyperactive can lead to energy being spent & hence no gain in weight).
From what you have described, it appears to be respiratory allergy or reactive airways, for which preventor/disease modifier medications are the main stay.
Poor response to inhalers might simply indicate that she may have been having uncontrolled airway inflammation which will take proportionately more time! Or poor techniques of taking inhaler/inappropriate medication
You need to point this out to your pediatric pulmonologist
Next Steps
Review with pediatric pulmonologist, for review/medication modifications
Health Tips
Breathlessness problem need not be there: only cough, especially when playing/exerting/at night