I like the stoics and their ideas, but my mind runs so fast when I'm extra anxious that it's difficult to put any of it into practice. I assume that's why it's suggested to do breathing exercises even when you're not anxious, so that it's more automatic when you are. So, I guess I should do more with stoicism when I'm calm.

My anxiety tends to be primarily about health and dying so I can understand your family member. Memento mori is good to keep in mind, except when you're in a panic about dying, then it just adds fuel.

I'd probably rather talk to your family member directly and be a sounding board, but it is probably better to start with the parents. I hope you can help, but don't get your hopes up, because as you know anxiety sucks and it's hard to absorb new information when your mind wants you to be stuck in misery.