Halfway through the second act of the musical “Mary Poppins,” a conclave of chimney sweeps bursts into a frenzied tap dance, followed by head sweep Bert defying gravity with a walk up, across and down the proscenium arch. It would be a show-stopping number, if only the production felt like it were going somewhere.

Instead the musical meanders for most of its overlong two-and-three-quarter hours, an episodic combination of bits of the 1964 Disney movie, material from the classic P.L. Travers books and inventions of the adaptor, Julian Fellowes (“Downton Abbey”). The sum is aimed at a family audience, though probably too dark in tone for the very young as it wades into domestic strife with a new story line about patriarch banker George Banks’s job being endangered by his making a risky loan.

The show, a first-ever co-production between the Disney organization and Cameron Mackintosh, opened Tuesday evening at the Kravis Center for a one-week stay. It is neither the best nor the worst to come from these two theatrical titans, but its six-plus-year run on Broadway (ending there in early March) says more about their marketing acumen than the show’s stagecraft.

Little was stinted in the gathering of the creative team. The direction is shared by Brits Richard Eyre and choreographer Matthew Bourne, who could have been more stringent when deciding what to trim from the show. The scenery is based on clever pop-up and fold-out storybook designs by Bob Crowley — winner of the show’s only Tony Award — here flattened and simplified for the sake of touring. And the earworm original songs by Richard & Robert Sherman have been augmented by some pleasant new numbers (like Mary’s signature “Practically Perfect”) from George Stiles and Anthony Drewe, best known for the musical “Honk!”

As you probably know, Mary is an otherworldly nanny who magically arrives, dispenses life lessons as readily as spoonfuls of sugar, is impertinent to her employers, but teaches the Bankses how to be a more loving, cohesive family before she grabs her umbrella and flies away.

In this hodge-podge evening, the garden statuary comes to life and Mary and her young charges, Jane and Michael, visit a word shop — yes, you read that right — where they do calisthenic semaphore to the iconic ditty, “Supercalifragilisticexpialidocious.” In an eminently cuttable scene, toys come to life and freak out the Banks kids and then there is a simple, endearing sequence of kite-flying.

Madeline Trumble is an aptly perky, self-assured Poppins, with a pleasant soprano voice and starchy manner. Con O’Shea-Creal is lanky and nimble as Bert, sort of a narrator/stage manager, and Karen Murphy makes a good baddie as Mr. Banks’ former nanny, sternly trilling “Brimstone and Treacle,” a counterpoint to “ A Spoonful of Sugar.” Kerry Conte does not have much to do as Mrs. Banks, but she makes us care about her pre-feminism plight in her one solo. The kids were way too shrill for my taste, but, who knows, you may find them adorable.

The bank chairman and his clerks keep singing about the value of “Precision and Order,” which are things this “Mary Poppins” lacks. But even more, it could use an injection of heart.