You're terrified of your parents becoming angry over you seeing this girl again . . . terrified. What's so terrifying about your parents being angry? You need to put some distance between them and you. Do you live with them? If so, you need to be working on getting your own place. Even while living there, you need to put some distance emotionally between you and them. It's simply not their business to be paying that much attention to your love life.

Wanting to break up, but stay friends, is wrong thinking. It's hurtful to her for you to keep hanging around in her life as a "friend." As heartbroken as she may get, she can get over it, if you leave her. You don't have to justify leaving her as something you must do for your mental health. It's perfectly okay for you to decide that you aren't happy in this relationship, want out and are ready to move on. Five months of dating does not give her some rightful claim on you. Next time you two break up, cut the strings and really move on. You may have to distance yourself a bit from her sister too. Cross-gender friendships among young, single people aren't always the healthiest of relationships. All three of you are at the stage of life where you are seeking mates. That needs to take precedence.

You are making very important decisions based on what other people want you to do, such as your parents and this girl. As you're discovering, it's impossible to keep them all happy. Focus on doing what is good for you.