An old Chinese legend tells of a poor little boy who loves to paint. He can't afford a paintbrush, so he draws instead. Then one day, he gets given a paintbrush by a magical old man - and whatever the boy paints turns out to be real. He helps his fellow poor people by painting things they need and eventually it reaches the Emperor's ears. However, the Emperor is greedy and wants only gold, and forces the little boy to paint things for him against his will. When the Emperor asks for a ship on the sea and some waves to go sailing, the clever little boy keeps on painting waves until they drown the ship, and then he simply walks away with his magic paintbrush tucked under his arm.
I read the story of the Magic Paintbrush to my son while he enjoyed an afternoon of free painting with my Water Brush. It's such a pleasure to watch children paint - it's a reminder of the truism that 'painting is one of the last freedoms' and nobody is more free than a child left to their own devices during cherished, unbroken and unstructured play time. It's one of the rare privileges of childhood and indeed it's what made me into the artist I am today.
I believe children should have a wide variety of art materials - both children's art materials and real, beautiful tools wherever possible. The mix allows them to go wild with materials while also learning respect for proper tools. Also, my raw wood handles encourage the tripod grip.
Let your kids play freely and allow them the space to be bored. Painting with kids encourages you to go with the flow too. There is no need to be prescriptive and there are no expectations - if they wants to dance with the brush on the page, let them. If they are frustrated that they can't draw a dinosaur and want you to do it, by all means step in. Many books and early years theories will tell you the opposite extremes of either letting the child do whatever they like and you keep your hands off (which can sometimes lead to frustration as they cannot fully express themselves without honed fine motor skills) or the adult taking over the act completely (where creativity is thwarted).
As an artist I say it doesn't matter. Just keep the flow going and what will be, will be. There will be other artworks, other times. Think long-term. This balance ensures that painting - or whatever activity you're doing, for that matter, with a child - stays playful. Sometimes it's a piece made all by themselves, sometimes they will want the adult to demonstrate, sometimes it's a shared piece, sometimes they'll want their hands to be guided, sometimes you keep the work, sometimes you don't. Sometimes they won't want to paint at all. Sometimes the paint disappears all by itself, as if painted by the Magic Paintbrush...