The sentence that has correct pronoun-antecedent agreement is:
Mrs. Smith was excited to teach her class.
In this sentence, "Mrs. Smith" is a singular female antecedent, and the pronoun "her" correctly agrees with it.
The other sentences have issues with pronoun-antecedent agreement:
- The twins laughed so hard she cried. (The twins is plural, but "she" is singular.)
- The brothers were getting along so well that he decided to go on a bike ride together. (The brothers is plural, but "he" suggests a singular antecedent.)
- The raindrops poured down, and it drenched the yard. (Raindrops is plural, but "it" is singular.)