I am married, but I don't have any children. My sister has two children, so she is busy with them in the mornings.
Sentence 1: The predicate (main verb) is "has", which is third person singular. Who has? ="my sister" is a noun used as a subject, and it is third person singular. The subject and verb in this sentence agree.
Sentence 2: The antecedent is the noun "my sister" in sentence 2, which is also third person singular. Therefore, the pronoun "she" and its antecedent agree.