I've had chickenpox when I was little, but I have no idea why I caught it a second time during a Vietnam trip (another student had it and I caught it) - so I'd say it's best to quarantine and limit contact whenever possible! The air-conditioning would definitely help your husband feel better, so you can probably keep that on :) Just to share that vaccinations are NOT miracle medicines, they do NOT give you a 100% guarantee that you will never get whatever it is you vaccinated against - in fact, vaccines itself are actually weakened/inactive versions of the actual thing you are vaccinating against - they just help your body to build a defence system around it so that if you do really catch it, it wouldn't be as severe because your body already knows how to fight the battle. This is also why it's common to have fever after a vaccine, because the body is fighting and finding the best way to combat it!
If they have taken the vaccine, they should be fine. If there are adults around him that have never had chickenpox or have not been vaccinated, they should not venture nearby. Aircon is fine as it will keep him more comfortable.
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I would definitely quarantine them, it is better to be cautious even though they have taken the vaccination. Air con is better since if it is sweaty it will add more to the itch
Yes, I would separate them anyway, just to be safe. Like the other mummy suggested, I would say to keep the aircon on to avoid sweating and itching.