"It's my dad," There's sometng genuine in that, a lot of Steph's life problems have revolved around her dad pulling bullshit. She hesitates again, but this time it's on purpose, "I think he might be having..."

Her persona would trail off there, so it's what Steph does. Her hypothetical dad is having a hypothetical affair with the woman Steph was trailing. It was a story that seemed to be the most reasonable -- accounting for the age of the woman, why Steph was following her, and the fact she didn't want to be caught.