Whilst I have to confess to being very
about the term "vibrant" when used to describe the OP's children, I also suspect that I know what she means.
Because whilst I behaved outside of the home/immediate family, as a child, whilst I was seen as docile, and quiet, and "the ideal child"... I certainly had my moments of causing havoc. I behaved outside of the home/immediate family because I was threatened, constantly, with physical violence by my mother. With my brothers and my grandparents, my aunt and my uncles, though... I could be me. I threw myself down stairs, off seven foot high assault course walls, off swings at their highest point onto concrete (child of the '70s, here, no safety rubber tarmac surfaces...). I disappeared for hours as a four year old across rural countryside, and was frequently returned by the guards on our estate for trying to escape it. I was undoubtedly "a vibrant child" in many ways... but I was also a very frightened, very angry, very misunderstood child.
Now though, now that I'm older, several of my friends like to leave their "vibrant" children with me, because they know that I can get them to behave themselves for a few hours (and give them a break). Want to know how I do that?
I engage with them.
It really is as simple as that. As a PP said, when children are encouraged to mop up their own spilled drinks, pour their own sauces, etc., they tend to respond to that. Children are children are children... but they're also expecting to learn how to be responsible from the adults in their lives. So when my friends dump leave their "vibrant" children with me, I make sure that I spend however long they're in my care for, talking with (not to) them, and doing things with them. It can be something as simple as baking cakes, or painting a picture, or letting them hold the lead of my elderly (and extremely tolerant) dog on a walk. Anything that gives them the impression that they have choices, and they have responsibility, and there's an adult in their lives who doesn't think that just because they're children they ought to be spoken down to/ignored.
Which, sadly, their parents do... as did mine, to me, actually.
Engage with your children OP, even if only in a different way, and you might find your friends/other mothers at the school gates stop telling you that they can get your "vibrant" little darlings to behave where you seemingly cannot.
for you, though, because we "vibrant" individuals aren't easy...