How did the Burnell children feel about the dollhouse?

The Burnell children see the doll's house primarily as a status symbol, an opportunity for them to show off how incredibly wealthy they are. Even at a young age, children are acutely conscious of economic differences; and if they're fortunate enough to come from affluent backgrounds they invariably want to let everyone see that they have the most expensive trainers, the latest smartphones, and so on.
It's the same with the Burnell sisters. Owning such a large, expensive doll's house immediately sets them apart from other children, reinforcing their snobbish sense of superiority over the poor, downtrodden Kelveys. The doll's house also gives Kezia Burnell the opportunity to defy parental authority, an opportunity that most children are only too happy to grab with both hands. Inviting the Kelvey sisters to look round her doll's house probably makes Kezia feel like a bit of a rebel. In any case, it would once again seem that the doll's house is being used for a purpose other than innocent play.

The Burnell children adore the doll's house they receive from Mrs. Hay. While the author points out that there are imperfections with the house—the smell, the pools of paint on the porch—the Burnell children believe that this just adds to the charm of the house. The author states, "The Burnell children sounded as though they were in despair. It was too marvelous; it was too much for them." They cannot believe their good fortune to acquire such a beautiful dollhouse.
The Burnell children are very proud of their dollhouse, not only for its beauty, but also for the attention it will garner them at school. The children, Isabel especially, are certain that the novelty of the dollhouse will provide them with extra attention from the other girls at school who wish to see it. Isabel revels in the popularity that the dollhouse has provided, and even Lottie enjoys entertaining the other girls from school at their home. It is only Kezia who genuinely appreciates the doll's house for its specialness and intricate details, regardless of the status it provides at school.