Rosalind had no idea what those two got up to over the majority of the summer but she did notice they seemed to grow closer as time went on when she joined them on the weekends. And that Izzy had more power over Julian because she convinced him to go do actual activities with her instead of hanging out in the library all the time.
The three of them would frequently go bowling or to a comic book store that had free board games for rent instead of simply going out to eat like before. It was fairly obvious that he was smitten already even if he didn't realize it.
That gave her the security to be herself a bit more, confident that nothing she did would be able to change the fact that her father liked her mother. She was a bit more outgoing in their group outings but still didn't seek Julian out on her own to be safe.