Prom ettiquette for next weekend?

I would wear the jacket when you go to the door. You can take it off shortly thereafter if you go in to sit down or when you get in the car. Parents always want to see the kids all dressed up. A handshake is fine for the dad, and a hug for the mom really depends on the type of person she is. You can't go wrong with a simple handshake for both. It is less awkward than trying to hug someone you don't know well. At dinner I would imagine there will be air conditioning. If you can tolerate it, you should probably leave the sleeves rolled down. All that being said, don't sweat all those small details. Just have fun.