First of all, your father’s sister is your aunt. Her husband is your uncle. However, because he is your uncle by marriage of your aunt, he is technically your uncle-in-law.
In-law refers to anyone who has become part of your family through marriage to a blood relative.
Examples:
- If Tom marries Sally, who has a sister named Chloe, then Chloe would be Tom’s sister-in-law.
- If your father re-marries someone who is not your mother, she will be your mother-in-law. When talking about parents, the prefix “step” is also commonly used. Ie stepfather or stepmother.