I adopted a cat, but now dad doesn't want her?

Dad is away 6 months of the year (in another city) so he is worried about the cat. I join him 3 months of it. Is there a way we can take care of the cat? They were going to kill her, so I took her in. She is extremely clingy which would be my other question. I read insecure cats get clingy, or when they’re very thankful to be adopted :( This broke my heart. I don’t want to let her go! She sleeps on me, stares at me all day, follows me everywhere, and is even super hesitant to meow. It’s actually ridiculous. I feel extremely anxious to have taken her home and rescued her but now have this incredible responsibility, along with school, work, and parents’ indecision. Help!