Pointing to Anil, Shivani said, "He is the son of my Father's only son". How is Anil's mother related to Shivani?

Sister-in-law

We have,

Pointing to Anil, Shivani said, "He is the son of my Father's only son"

This means Shivani has only one brother and Anil is the son of Shivani's brother.

So Anil's mother will be Sister-in-law of Shivani.