If I were in your situation I would help your sister find a new place to live. If she can afford to pay for a place of her own, I don't see any harm in that. Just explain to her where you're coming from and hopefully she'll understand. You're name is the only one on the lease so she doesn't really have a say in the matter... I understand that you love your family and don't want to cause any harm, but if your living situation is causing problems for you, then you've gotta have a talk with your sister and work it out. You don't have to be an asshole about it, just explain the way you feel and I'm sure she'll understand. I wouldn't say the following to her, but just keep in mind that in the end it's up to you (as the lease holder) who lives in your home. You can't move out so you have no other option. I'm sure you already know this is what you have to do, and I would agree that it's your only option if you want to have a place of your own.
Peace