How do you learn how to live with being apart from your kids without going crazy missing them?

I don't actually have kids yet, but my mom has pretty severe depression and my dad travels a lot and so I've been taking care of my 13 month old sister since we brought her home from the hospital. People were actually shocked to find out she's my sister and I'm not a teen mom because pretty much every time I left the house I brought her with me. I went to school online and was home all day with her. I'm the one she wants when she's upset. I think she thinks I'm her mom too. My mom doesn't give her a lot of time or affection. I'm spending the summer with my grandparents and I'm thinking of staying here for my senior year of high school. We're Americans but my family moved to Australia for my dad's job a few years ago, and I've been miserable there. I really do feel like I'm going to go nuts here sometimes because I miss the baby so much. I worry about her all the time. I miss my other sister and my brother so much too it really hurts. I can't even sleep sometimes because I just miss them. I can't just go back. It's complicated. My grandparents said to not worry so much and enjoy the summer. They really want me to stay here with them till I graduate because they know how messed up my life has been in Australia because of my mom. I am happy here, much happier than I've been in years, but I miss my siblings so much I really don't know how to cope. I really do feel more like a parent than a sibling to them. I don't know how to overcome this.