After 10 years of trying to cure her condition that sends her to a different parallel universe every time she falls asleep, a obsessive girl finds herself returning to an alternate Earth for the first time and must work with an alternate version of her scientist father to discover the secret to controlling her ability in order to return home.

Apathetic? I'm not sure this is the best word to describe a protagonist. This suggests she shows or feels no interest - so why does she care about getting home? I appreciate what you said about home being where you belong, but I think there might be a better word than apathetic.

It makes me think of Quantum Leap a lot. He was always searching to get back home and never gave up hope. I think the same needs to be said for her. Currently all the events that have happened to her make her a passive protagonist, she hasn't had a lot of choice. If you make it so she's always fought to find her way home, always been proactive, then I think the audience will feel more when she finally does get back home.

I kinda don't want her to get home until the act II climax. So we see how she's actively trying to get home and it makes the moment she does that much more powerful. I think it'd be really cool for act I to be her ending up in the first parallel world, act II rejoins her 10 years later, but she's got like a big book full of clues and information that she's accumulated, and although she's weary she's never stopped fighting and that's when she finally connects the dots that leads her to something (a macguffin) that enables her to get home at last.

Think it's a really interesting idea! Looking forward to seeing where it goes.

You can drop the 'lab rat' part of the logline. Finding her father before she falls asleep is a strong enough premise for the logline.

What is making it difficult to find her father? Is there a way to make it seem like her goal is going to be very difficult to attain?

Is her time in each universe actually dependent on her sleeping, or is there a time that she teleports - like midnight?

I like this idea very much - very best of luck bringing this to the screen.