Open Pet Adoption?

So I found this puppy and reported it to Animal Services and posted online and took it around the neighborhood, etc. We've had it here about 3 weeks and we've become very attatched. Yesterday, a family shows up and asks for their puppy back. All the kids are really upset, and so am I, especially because she had an advanced case of worms when we found her, was unregistered and sickly.
We are all in love with her, especially my old dog, who's often bored out of her mind, when we are busy.
My boyfiend & I have been looking into the protocall for puppy-care, i.e. worming, vaccinations, spaying, registration, crate training (she has a house-pooping problem), and how much that all costs and what it requires; and feeling like this dog should have had all of that before it got a chance to end up running around in the street, dying of parasites. I couldn't bring my self to give her up without a guarantee that she'd be properly looked after. But it was breaking my heart, because they were clearly as fond of her as we are.
I feared there was no easy answer.
Then I learned that the family was just about to take a road trip, and I thought, Geez, there's plenty of time to discuss this after their trip, without a bunch of upset kids hopping around, freaking out, climbing all the fences & spilling out into the street...Whew!
So I asked for their phone #, & if we could discuss it when they got back.
The lady's response surprised me. She said the puppy was clearly very loved and happy, and that puppies are like little kids: they need to run and play, and we have a bigger yard, and we're obviously very nice to her. She said she'd bring over the dog food & jackets they have for her at home, and she asked if her kids could come visit.
That was intense. The kids were really nice, and about the same ages as my kids. They actually fit in really well, at my house. But how often do I need a storm of that kind of energy, when I already live in that climate?
It's really kind of a commitment. But here's the thing: My 4yr old has very few friends in the neighborhood, and it could be a really good thing.
So the puppy looks like she's staying here.
Here's a weird thing: My 11yr old acts like she "won." She decided that she hated the girl who lost her dog, and heard everything the girl said as mean and ugly. I saw a very nice and polite kid, about my daughter's age, who misses her puppy.
When we discussed it among the adults in the house, we made the "other" family into a cartoon "Other," and said comically ugly things that were utterly outrageous, like, "those weren't worms, they were balloons of heroin. She was being ABUSED!" (I didn't say that in front of the kids, by the way...) But of course I didn't actually hate them, I was trying to separate my possessiveness from my protectiveness, using humor to sort out my feelings. But my kid just really hated the "Other Girl." That made me sad. I guess they should hang out...