Hi, Pianochick. This does sound like a toughie ! There are a lot of things involved within this, some of which have been hinted at by others here. There is a lot that we could talk about with regard to family relations and family dynamics in this situation and that could be helpful, too, but since I already feel like I have a lot to say I will aim to touch on "just" the teaching aspect of what you are doing.
What you are taking on in deciding to teach your sister piano is actually a very mature decision. It takes a lot of organization and constant growing on your part to really do it right ! It also takes a sincere commitment to music and to your students to want to put in the effort that is required in finding different ways of explaining concepts to each individual (and to deal with their parents at the same time

!). I can only imagine what parenting must be like (okay, I actually have some pretty good ideas

) !
May I ask you, do you wish to make this a profession ? And, if not a profession, are you wanting to be teaching for awhile ? In any case, what are
you hoping to gain from the experience of teaching in general (not just from teaching your sister) ?
Whatever you are hoping to learn from the experience of teaching will greatly impact what kind of teacher you are for your students. There are definitely certain things that I feel I am claiming about myself as an individual by taking on the profession of teaching (and not just of teaching in general (though that, too) but of teaching music/piano, specifically). Some of that also has to do with being a woman, specifically, too.
One of the most important and helpful things I have found in teaching is to make studio policies. Even if nobody else ever saw them (though they do see them), I find that just the act of clarifying to myself how I want this experience to go is a very empowering experience in and of itself ! It's fun, too

. Perhaps you would enjoy making some policies of your own for
your studio

.
What I find fun about it is that I get to map out what my ideals are (at the time) for my business, and I do just that; I give myself permission to go with my true ideals. I have always found the courage, after clarifying these things to myself, to show these to each family that walks through my door. I used to be always surprised when people agreed to them because they are essentially agreeing to my ideals (imagine that !) !
When somebody who was already enrolled within my studio would question them, yes, I would take some time to (privately) review my thoughts on these matters, but I would always end up falling back on what the policies state and would then be able to just feed these people the rules and guidelines involved with being a part of my studio. The policies were the authority and all I had to do was follow them.
I think in many cases, or perhaps all, the greatest defense is a strong offense and, everybody is capable of that ! Everything you do now will only strengthen and clarify who you are. Even if you don't make teaching a profession, your effort in discovering how to craftily cope with these circumstances will not go to waste. The key is in knowing that there are already answers for you, and there are.
Well, there is a lot more to this but I think I have said enough for now. As a lengendary forum member used to write, this is just the tip of the iceberg

.
Best,
m1469