My mom is still sick.

I helped her with the dishes.

(In the sentences, what is the meaning of the second sentence? Did her mother washed the dishes with her daughter? Or did her mother not wash the dishes together?)

The second sentence means that she and her mom washed the dishes together.

In the second sentence, "I helped her with the dishes," it implies that the speaker, likely the daughter, assisted or aided in the task of doing the dishes. It does not specify whether the mother also participated in washing the dishes together, but it indicates that the speaker provided assistance in some way.