Is the husband entitled to intervene in worldly matters pertaining to the upbringing of children, such as food and clothing? And would the wife be sinful for disobeying him in that?

If the disagreement between spouses regarding a child's upbringing concerns their food and clothing, they should refer to the Shari'ah evidence and ask knowledgeable scholars if the dispute is about their permissibility or impermissibility. However, if it concerns the types of food and clothing, then custom should be referred to. If the husband insists on a specific matter, then his word prevails, and you must obey him. The wife should gently and wisely persuade her husband. Both spouses should make concessions within permissible bounds to maintain affection and improve their situation, for contention leads to discord and poor upbringing of children.