I think the type/breed of the dog is important info missing here. The age also might be helpful to know. But regardless, time is needed to adjust to a new situation. Don't push any interactions and give as much space as needed. After enough time (which will vary greatly from dog to dog) the dog will become more comfortable with your new prescence.

Not expert, just adopted my first big dog, year old labradoodle who wasn't getting enough time from his previous family - they had two kids and then had twins and right now he needs a lot of attention and training which they didn't have the bandwidth for. Wonderful people though and they did the right thing finding us. He has a few barking and playing-too-rough-with-the-tiny-chihuahua-and-cats issues we are figuring out, but overall it's always clear where it's coming from when he's misbehaving and he's a good loving dog in the end. He's also only been here slightly more than a month and I'm told it takes three before they're really settled, so we have high hopes.

Is this when your parents aren't home? Or when they're around? Could mean different things. Some dogs tend to be one-person dogs who tolerate those who live with them and have no interest in anyone else. Breeds affect this kind of thing too.

If she likes to fetch a ball or some other toy, then giving her some exercise followed by some basic commands (come, sit) with small rewards for doing what you want will go pretty far.

Exercise, discipline (always positive reinforcement, never ever hit her), followed by affection. She'll see that she can trust you and will relax.

As some others have said, go slow and don't force any interaction. Maybe involve your parents in the exercise and discipline parts.

If she's a rescue, then sometimes they just need time and consistency to come around. You never know what a rescued dog has been through before becoming your pet. Something you were doing or wearing could have set your parents' dog off that was in no way intentional. Not all humans are kind to their animals - some are downright evil. I had an ex-girlfriend who had a sweet black lab who was terrified of men, those wearing hats and boots in particular. With some time and lots of love, he came around.