Let me start by saying that there are so many great responses in here that I think you should heed. I don't doubt your fears, what your parents may be capable of, and especially not the real risk that FGM may be the true intentions of this trip. This is a huge disclaimer that I consider FGM 100% abhorrent and unacceptable. I am merely trying to address a contingency that I don't think has been covered by the many great responses. I AM NOT SAYING THIS IS THE LIKELY CASE. ONLY THE OP HAS THE FIRSTHAND KNOWLEDGE TO DECIDE WHAT THE LIKELIHOOD OF THIS SCENARIO IS, OR IF IT IS EVEN A POSSIBILITY.

(Please for the love of hell don't downvote me to oblivion, other redditors. OP needs to consider this. If she thinks this possibility is unlikely, then it is unlikely and I have no reason to disagree).

OP, I am talking about the possibility that this trip was NOT intended to subject you to FGM. Your parents work in a western nation as healthcare professionals, as you describe. Their reputations and careers can be ruined if they are FALSELY and PUBLICLY accused of intending to subject you or your sister to FGM, since it is rightfully considered barbaric.

Whatever course you choose, you should put the safety of you and your sibling - as well as the integrity of your bodies - FIRST. I know this will not be easy, as you say you cannot trust their responses, so I would suggest that, as long as you still do not know your parents intentions 100%, any external help (e.g. FGM helplines) that you seek should be from organisations and other people that will respect your confidentiality, in addition to helping protect you.

Again, if tomorrow you find they admit to it, or you determine yourself that FGM is 100% the intention of this trip, you should NOT worry about your parents careers, and you should first protect yourself and your sister in any way necessary, public or not.