"Mi hermana se lo da" is correct and the pronoun is replacing "yogur" so the "su niña" complement would still be necessary for the sentence to make complete sense. It would be " Mi hermana se lo da a su niña".

It's referring to "mi hermana".

I believe the "le" is referring to "mi hermana". I am a student of spanish myself but i believe that is correct.

After some research, I believe in the original sentense, le actually is referring to "su niña". I found some examples in my text book under the indirect object pronouns sections. e.g. Yo le compré un regalo a victoria. I bought Victoria a present. Pedro te habla a ti. Pedro is talking to you. These are similar sentence as "mi hermana le da yogurt a su niña".