The text on the first page is "Some children get new clothes. Others have hand-me-downs... Or their clothes come from charity shops."
Now, here's a larger image of the children under the "Fancy Dress" sign.
Clearly, the children are meant to be in costumes, playing dress up. As you see, one child is dressed up in what we're meant to see as an "Indian" or "Native American."
Update (1): Shortly after I published this post, a reader wrote to say that their copy says "Costume Party" instead of "Fancy Dress." They have a 2010 copy with a "reprint" year of 2011. I wonder when and why that change was made? I assume the original said "Costume Party" and that someone objected right away, and so those words were changed to "Fancy Dress." It doesn't make a difference. We know what they're doing. What it is called doesn't matter.
Update (2): Celeste submitted a comment that I'm inserting here because it may explain the differences we're seeing. Celeste wrote "The difference in language might be a British/American edition thing. British English uses "fancy dress party" where American English uses "Costume party." Inexcusable either way."
The problems in that choice are many. First, it is a stereotypical illustration. Second, even if it were accurate, it ought not be shown as an option in an array of dress-up costumes.
Regular readers of American Indians in Children's Literature know that I suggest a radical action for books like this: take out a marker and fix it the text. But that won't work in this case. The best option is for the illustrator to revisit the page and remove that illustration.
It reminds me (and maybe you, too) of the Alvin Ho book I read some years back. People may feel they're honoring Native peoples by dressing up in something they bought at a store (like Alvin did), or that they created using a craft store kit, but please don't do that.
Some might argue that kids dressing up like that is an accurate reflection of what kids do, and it is, but it should not be something they do! Books like this reinforce that play and encourage stereotypical thinking about who we are---and that, of course, is a problem! Dressing up like that is similar to the mascots that were created to "honor" Native peoples. If people really wanted to honor us, they'd hear us when we say "stop doing that" instead of trying to defend what they're doing.
The Great Big Book of Families is much-loved by a lot of people because the author and illustrator included families with two moms or two dads, and because the people in the book are a range of skin and hair color. People will likely think that the child in that headdress is insignificant. I don't think it is insignificant. Stereotypes of Native peoples are not acceptable. They can be harmful to Native children's sense of well-being, and they affirm or misinform non-Native children about who Native peoples are.
The Great Big Book of Families is not recommended.
