I rarely drink but it doesn't bother me to be around alcohol and I don't care how much anyone else drinks.
That's a control issue imo. It's not my place to decide if someone drinks, how much they drink or when they drink - that's 100 percent up to them.
Them handing you wine without asking is out of line. I would actually call them and mention it (if you are so inclined).
The shaking is definitely an emotional reaction and worth working on. Not because you need to feel comfortable around alcohol, but there is obviously some trauma there.