Greetings to the Original Poster. My wife received her cancer diagnosis a little over a year ago, and since then I've been her main caregiver full-time (administering meds, driving her to appointments, cleaning up vomit, etc.) One thing I've learned since then is: when in doubt about medications or food or supplements, ask your doctors. Not just those in Hem/Onc, but the Radiation doctors, ER doctors, attending nurses, etc. Regarding kava for anxiety during cancer, my suspicion is that there are better pharmaceutical-grade options out there with well-studied interactions, but the best people to make that call are medical specialists with knowledge of your sister's particular status and set of current medications.
As a caregiver for someone with cancer, I should say that kava has helped me tremendously. It's helped me manage my own emotions enough to get the job done, without clouding my mind or inducing sleep. I'd already been prescribed a stimulant and an 'as needed' anti-anxiety pill. But Kava helped me handle things like putting my career on hold, dealing with panicky in-laws, listening to hurtful things my wife said when she thought she would die, and - perhaps hardest of all - helping our kid deal with what was going on.
That being said, I wouldn't necessarily recommend that anyone start kava while caregiving. I started taking kava years ago because a bit of it tasted good in iced tea, it put me in a good mood, and it made me really enjoy hanging out at home cooking dinners for friends. Along the way, I noticed that with some kavas, trivial things that previously would have bothered me didn't bother me as much any more. Over the last year, I noticed that a bit of kava in the morning with breakfast and later with dinner helped me deal with some pretty stressful situations without turning me into an unemotional robot or a giggling fool. But there were some things that kava alone couldn't handle. And I wouldn't claim that my own subjective relationship with kava would automatically translate to anyone else.
p.s. Sorry I didn't respond right away... halfway through my first response my wife started vomiting uncontrollably, and during my second attempt her blood pressure dropped so much I had to call an ambulance. I'm almost afraid to check in on her now...

Anyway, good luck, I wish you and your sister the best.