What is the "inhalation" she is getting for the cough? Is it an over the counter medicine or a prescribed inhaler such as for infant asthma?
some of those can stop them sleeping. Can you move the inhalation to much earlier in the BT routine, say before bath time and the usual wind down so that it isn't so close to sleep time and doesn't disturb her regular WD?
During SA the best way is to be with your LO as much as possible, accepting that they need more cuddles, more help, more time, is really the best way to help them through it and for me once I accepted what I needed to do it was far less frustrating for me too.
I've always found that having more hands on with stroking or rocking in the bed or keeping a firm hand on etc has not ruined my DS's habits. Generally once the SA phase passes they just return to not needing you as much, or it is a very simple short wean of the additional help.
I've also, a few times, just shifted my DS's BT later, it if was taking him an hour to go to sleep I've moved BT say 30-60 mins later to reduce the amount of time we are up there, even though I know he needed the sleep. Again, once the phase had passed I was able to bring BT back to it's regular time.
Another thing I've done (so long as he wasn't actually crying) is set up a book and a coffee outside his room and made myself comfortable expecting to be there 30 - 60 mins giving verbal support, in my DS's case it was "it's night time, go to sleep" and "everything is Okay, I'm right here, go to sleep" and repeated many many times when he called for me but was not actually crying or distressed.
Try not to worry about habits too much, LOs going through SA do need extra support because of how they feel. It will pass eventually.