Some serious over-reaction here.
I have a small prescription of diazepam now and again from GP to help with my fear of flying, to be fair it enables me to cope with it a bit better; although I still think we are going to crash, I just don't care whether we do
. My GP didn't check my health in anyway before prescribing.
My DH has one of my tablets before having a blood test twice a year, he is phobic about blood.
To set your mind at rest, I would check the contra-indications of the drug. If your DH is a sensible person in other ways, and has no major health problems, and not taking any other medication and has not ever had any addictions; I personally think you are being a bit silly and precious. He needs to avoid alcohol when taking.
Just be aware that after taking a tablet you can be pretty useless at helping with organising the process of travelling, so if you need support with DC or negotiating through the airport don't count on your DH to be "totally present". He may also be vague for the next 12 hours or so and must not drive after taking one for the same amount of time.
It does sound like you are pretty anxious about this, it might put your mind at rest if he gets his own prescription, although not absolutely necessary tbh.