"Why do people think that it's cute or funny to ask little girls (with big brown eyes) if they can take them home, or if their mom would notice if they took her little brother away with them? And then they have the audacity to expect that little girl to give them a polite goodbye or even a hug? My daughter is almost three and is a bit of a thinker. I always assure her after the fact that I would never let that happen. I don’t think I’m being too sensitive, or too protective. I wish I could think of a good snide comment to make in these situations, but these people are frequently the care givers at my mother-in-laws Care Facility that we see on a semi-occasional basis and we rely on their goodwill. Any suggestions on how to handle these situations?"
What is wrong with people?!
There are a bunch of different ways to handle this kind of thing (and I'm sure the readers will have some suggestions I haven't thought of), but there are two main goals behind whatever you choose to do: 1) You daughter (and son, later) needs to know that no one is going to try to take her away, and 2) the person saying it needs to know that it's not a smart or OK thing to say. Other than that, you have to judge the person and situation and adjust for that.
I've never actually gotten a comment like this that's sort of in the nebulous zone. I get comments all the time from people we know (neighbors, etc.) saying they'd like to take my younger one home for the night, but they never say it to him and we all know they're just joking, so my standard answer to that is, "You'll change your mind at 3 am!" and we all laugh. It would be different if they were people my kids didn't know well or were talking to my kids instead of to me.
I've also been approached by strangers trying to talk to my kids in public in a harrassing way. I start with, "Please don't talk to my child. It's threatening." If the person is a decent human being, they apologize and back off. If they keep approaching us, I take their picture very deliberately with my cell phone and tell them I'm going to call 911 because they're threatening to harm my child. I've only had to do that twice, and both times the person ran off before I could dial the 9.
The problem with your situation is that you have to be nice to these people, and they don't mean any real harm, but it's scaring your daughter. So I think I'd just expose the whole situation for what it is at the time. When someone makes a comment to your daughter, you could respond to your daughter, "Oh, honey, I know it scares you to think that someone might try to steal you away from home. Ms. X didn't want to scare you. She's a very kind person, and she'd never try to take you or your brother home. She just meant that she thinks you're such a nice little girl. She didn't realize you were too young for teasing like that. She won't say it again" Then turn and smile at the person who said it to show that you're not mad. Most halfway-intelligent people will figure out that they scared the crap out of the kid and that they shouldn't say things like that again.
I think the good that will come of bringing it all out into the open is that your daughter learns that you take care of her, that you can fix a lot of situations just by making the assumptions explicit, and that it's more likely that people are just inept than malevolent. The hope is that the people saying these things will also learn that they're indavertently scaring kids, so they'll rephrase their admiration into something less scary.
(Once your kids get to be older and more able to distinguish between real threats and idle idiocy, you can use what my mom has always said when someone wanted to take us home, which is "It would be The Ransom of Red Chief.")
Hugging strangers goodbye? No way. "She's not a hugger," in a breezy, unconcerned voice that allows no arguing. We have friends who taught their daughter to blow kisses, and they'd use that to charm people but make sure their daughter wasn't ever even remotely guilted into physical contact with anyone she didn't want to touch (including over-eager grandparents). It's never too early to reinforce your children's rights to have their physical boundaries respected.
It's enough to worry about actual dangers to kids without having to deal with thoughtless comments that can scare them, too. Let's heave a sigh of exhaustion at the stupid things people do, and then go back and reread Protecting the Gift by Gavin DeBecker.