If you have time before you do it, you can practice. I've done this for meetings and presentations that I anticipate will be difficult. I start by imagining what someone else would do ("how would my competent friends handle themselves in a meeting like this?") and then try on different versions of myself, if it's not immediately obvious what a braver version of myself would do. (I often have that problem.) It's like what Brienne describes but over a longer period of time, so you can take advantage of habit formation. Then, if you have what you'll say and how you'll say it well rehearsed (not memorized, but rehearsed), it's easier to go into the difficult situation sort of on autopilot. You can keep Brienne's technique in your back pocket if the autopilot fails.

The downside of rehearsal in your head is that you might find yourself dwelling on all the horrible things that could happen. This is usually where my mind goes if I let it because it's easy to let the models I have of other people run amok and show me all the worst possibilities that I might have to face. You have to just rehearse the part you know you own and not spend too long imagining in vivid detail what happens next, besides what is useful for preparation (like what beoShaffer suggests and similar practical plans). I hope it works out for you and you'll let us know how it goes!

How did it go? Were your family okay with it? Was the technique effective?