Is it haram to take a jacket from the school's lost and found, instead of a lost jacket belonging to one's daughter that is difficult to find?

You are not permitted to take another garment in place of your daughter's lost garment, even if the person in charge gives permission, because lost items remain the property of their owners. Therefore, return the other clothes and search for your daughter's garment. If you do not find it, do not take anything else. The possibility of the owner of the large jacket mistakenly taking your daughter's jacket is remote, and students can be asked about the jacket. This issue resembles the issue of lost sandals in mosques, where a replacement sandal is considered a "luqatah" (found item), and its owner must search for their original sandal, not take another's.