Thinking about Padlock as parents and just remember this scene from one of the Addams Family movies where Wednesday comes out with a knife and when she confirms she's going to use it on her brother, Morticia takes it and gives her a bigger one. Change "brother" to "friend" or something similar, and I can see that happening with Paige and June.
June has a strange affinity with human children that her parents don't quite understand. Perhaps it's because they're all around the same age, or because June was born surrounded by humans. When she asks if her little friends could come over... Why not?
Of course, there's one fatal flaw to the operation: Concept play is very different from human play, mostly due to the fact that one species is capable of rising from the dead, while the other isn't.
Paige and Tony seem to leave that as an afterthought, and little June barely understands how her and her parents can die and come back, but her friends somehow can't. So, of course, she invites them to "play swords" with her, leaving them unaware that they're talking about real, child-sized blades her father gave her.
Or maybe play house, which sounds fairly normal until she starts to play-duel her friend, or play-poisons their food because "that's what mommies do! Now pretend your hands are shaking, that's what happens first when you get poisoned."
(Pause for Paige to have her proud mother moment.)
Of course, many kids in the neighborhood think June is like, the coolest kid ever. Her dad gives her real swords for her birthday! She knows everything about fighting and poison! She has a real heart in a jar in her room!
Some boys might even have a little crush on her, but they'll never say that out loud, because June's dad is really scary when the grown ups aren't looking. In fact, most children who went to June's house have seen Tony and Paige's concept forms as soon as their parents turned their backs. But what parent is gonna believe it when their kid comes home saying little June's parents are immortal and can shapeshift?
"Mom, I'm serious! Her hair is super colorful and moves out of nowhere, like she's Medusa!"
"You know that scar June's dad has on his face? It moves, I saw it! It was pointing down and then it went up, like a clock when an hour passes!"
It's not like they make a big deal out of hiding it, but adults usually don't believe in magic.