What tools does a Buddhist have to engender others to take a wiser approach? Mum is regularly woken in the night by panic attacks which bring on uncomfortable physical sensations that she takes so seriously she has been known to ring the paramedics (always unnecessarily). After many months I am still unable to get her to even entertain the notion of 'staying with the discomfort, just as it is'. Does a Buddhist have any tools (metta/prayer/mantras - sorry I don't know the words) to manifest/stir-up a change in someone else’s approach? Or do I have to work on cultivating my own acceptance of the situation - however resigned that might make me feel?
I'm sorry to hear about your mother's discomforts. I used to have similar panic attacks that would bring on hyperventilation, taking Xanax and in extreme cases calling the paramedics as well, even though I had studied Buddhism academically for many years and I "knew" it should be able to help me.

It was only when I actually started practicing in stead of studying the attacks subsided, mostly because I had learned to recognize their arising in my mind and the cascade of thoughts, feelings and physical reactions that followed out of them.

The best recommendation I can give you from personal experience is not to start with "staying with the discomfort", as this already requires a person to be able to "witness" the arising and setting of thoughts in the mind. I suggest you start with simple breath counting in a comfortable position and once she is comfortable doing this, ask your mother to observe the space in between thoughts. Doing so will allow these spaces to grow and allow your mom to see the arising of thoughts and sensations, in stead of them being constant and unstoppable, like we usually perceive them. Once you get to that stage, you can start focusing on "staying with" the discomfort, as she will no longer experience it as inevitably leading to the subsequent discomfort in her mind.

Hope this helps, best wishes to you and your mother.