I am amazed at your wisdom to evaluate the situation peacefully and objectively. I have been in a similar situation, I wish I had your maturity back then. You will do fine, you will find a way out of it, and come out stronger.
You have a practical problem to solve – how would you support yourself and your sister, considering you are still a minor. Talk to a social worker in your area. There is help out there, you just need to ask for it.