I probably shouldn't even be commenting, since I'm not an expert, and I'm not familiar with Brincanyl (Turbohaler, I presume).

However, it sounds if you need to speak with your doctor, as he or she may not realize that your daughter cannot properly inhale the medication when she's sick.  (I always find it ironic when the instructions say to breathe in deeply when one cannot breathe!)  That said, if you happen to have a nebulizer, I see Brincanyl also comes as a nebulizer solution, so perhaps that would be a more effective means of delivery when your daughter has difficulty inhaling the powder.  Otherwise, I would think your daughter could be switched back to Ventolin, but I have no idea, of course, why she was switched off it in the first place. 

Also, in case it helps, I have always found that Tilade or Intal (but particularly Tilade) is very effective, for me, in quelling the cough due to asthma. (Don't know if that is the problem or not.)  Both Intal and Tilade have virtually no side effects (in most people), and Intal also comes as a nebulizer solution -- cromolyn sodium inhalation solution -- made by Teva: http://www.tevausa.com/default.aspx?&pageid=76&brandName=Intal%C2%AE%20Inhalation%20Solution, which is a generic and which I have found to very inexpensive. 

In any case, good luck.