Yes, they do. They also know that their priest gave her a sip of wine at her first communion. I guarantee she got more alcohol that day in church than via the small sip I let her have. I can't answer the first part or your second question but I see nothing wrong with this picture. One sip of an ice cream beverage loaded with whip cream wasn't going to hurt her. Have you seen how much alcohol (or lack thereof) they put in those drinks?
Because my niece was enjoying the pool when I ordered MY drink FOR ME. And I was quite enjoying it while lounging in my chair until the kids (and DH) came back. My toddler grabbed for my drink and my niece wanted a sip too. I suppose I could have said NO, NO, got up, walked to the bar, stood in line, ordered 2 virgin drinks, walked back, handed one to each and apologized profusely to all the poor people who just endured my screaming toddler who wanted a drink of my "smoothie" 10 minutes ago, but why? One little sip (primarily whip cream) wasn't going to do them any harm. My niece liked it so the next time I went to the bar I got her a virgin. Of course, my son wanted a sip of hers too! I tried hers and frankly I couldn't taste a difference

I rarely drink, but don't mind indulging in a few fruity ice-cream drinks on vacation.
I don't need to. My grandmother raised 10 kids on a farm in rural Tennessee. Do you know what they used to do for teething infants and toddlers back in the day? They rubbed whiskey on their gums. And none of them wound up to be friends of BillW. Yet, that's more alcohol than my son (or my niece) got from one sip of my fruity ice cream drink. His pediatrician recommended Benedryl when he was teething. I think it has some alcohol in it too.
To everyone else: I cannot believe some of these replies. I just wanted the OP to know that what she asked didn't seem like a big deal to me. But I guess we live in way too uptight a society for people to get so bent out of shape. Judging from some of the replies you would think I gave the kids crack.
And to those who suggested that I'm somehow a bad parent for doing what is easier, I assume you have never given your toddler candy, soda, toys, etc. when on vacation in order to avoid a terrible two's tantrum? Good for you! I choose my battles and don't sweat the small stuff. One sip to me is small stuff! Sorry you feel differently but my parents raised me and my sister the same way and we turned out quite well.
BTW, I think there is a reason why Europeans have less problems than we Americans do. They are less uptight!