Why are the twins upset that their mother allows the old woman in during the evening?

Sandy and Dennys are the sensible members of the Murry clan. Unlike the rest of their family, they're practical, down-to-earth, and just so incredibly normal. Since their father left, they've appointed themselves protectors of the family. That's why they chide Meg for getting into a fight at school; if there's any fighting to be done, they'll do it.
Mrs. Murry's decision to let a strange old woman into the house—Mrs. Whatsit, no less—doesn't exactly meet with the twins' enthusiastic approval. Inviting strangers into your home, especially what appears to be an old vagrant, just isn't a very smart thing to do. Sandy is adamant that his mother needs him and Dennys around to protect her. After all, says Dennys, that's what their father would expect them to do. Sandy patronizes his mother by telling her loftily that, although she's smart, she doesn't have much sense. The same also applies to Meg and Charles.