I really wanted to know what happened to them in this timeline. Did their parents accept their affair? This timeline is the one where Ilya didn't do anything wrong, so to speak. She didn't lash out to her sister or anything. Surely the parents took her side... Right?
I mean, to me communication is the key factor in all timelines.
She keeps holding in her thoughts, not expressing what she's thinking, and not resolving issues that could be solved with discussion, or even collaborate with outside help.
We don't get to see the full picture of all the iterations because this story is being told from her perspective, and she's an extremely unreliable narrator. Compound that with her terrible communication skills, I'd say it's correct for the story so far to NOT show her parents actions, or any character's motivations outside of the FMC for that matter.
But I think you can guess based on what's shown (e.g. no, the parents didn't take her side, because she did not properly communicate with them and establish a solid relationship with them, thus why they aren't even mentioned in the iteration, aside from setting up the bars).