The first thing that needs to be said is that the circle in this brand belongs at the top, as shown below. This brand is sometimes shown with the circle at the bottom, which is wrong.
Our opinion is that this symbol was probably based upon early Christian practice. The circle has been used since ancient times to symbolize eternity, a meaning adopted by the early Christians. It isn’t as clear what the bottom is intended to depict. It may be a symbolic tree signifying life, which together with the circle would mean eternal life. You also sometimes see the bottom portion of the brand done with straight lines, more like a cross. The circle and a depiction of a cross were frequently used together, signifying the persistence of Christianity for all eternity.
If your daughter’s teacher has another answer we would love to hear it. The answer we have provided reflects the opinion of three mission scholars who between them have written about a dozen books on the Spanish missions but none claims to be an expert on cattle brands.