It's not easy to hold the unpopular opinion. But something that I could suggest if this happens again is to just remove yourself from a situation like that (if it happens again).
First, it's difficult having your entire family ganged up on you for your difference in believes. Trust me I lived that s-it all my life with my effed-up JW family. Not once I saw anything good coming out of a situation like that, and chances are that it's very difficult to deal with it, especially since those are people you live with every day. Handle them all at once like I did at some point, but only when I was in a position of complete independence from them. Some family members just don't drop it, so avoid that situation; it's not going to bear anything positive.
Also, please consider what seems to be the thing people in this forum tend to forget about the most: their feelings. Forget about doctrine, forget about the new light nonsense, forget about them changing their minds and wanting to be right all the time about everything. Think about them all, collectively, as a family, having to admit that you are right, and that the organization they rely on and trust is just top notch BS. Under those circumstances, admitting that you are right, or having some kind of awakening is just not going to happen. It's not productive at all under those circumstances, especially if you pay attention at what they feel, and the emotions that are implied with them all being wrong for so long about so many things, after making so many important life decisions around it. It's not just about what the WT teaches. It's also about how they are told by them how they are supposed to feel about themselves and the world around them. That is the fundamental cause of the cognitive dissonance that you saw happening (your sister jumping in to tell you how that organization is "the true religion" out of something completely unrelated to what you were discussing). Their feelings, not their knowledge, is what causes them to do that.
Second, I think that you yourself are in a place where you need to take care of you, and only you. I think that you should prioritize in what you are learning, but also in what you are feeling. As clear as you see it, and as full of s-it that the WT teachings are, I think that you may need some time yourself to deal with your own relationship with the WT and how your awakening impacts you, your life, and consequently, your relationship with your family.
There are a number of emotional battles ahead if you want to remain a JW (for now) at the same time that you realize all the BS that they try to shove down your throat. That should have priority over trying to make them see the light. In this instance you were shamed, shut down and made feel as if you are doing something wrong, which you are not. And the fact that they were the ones ending the conversation reinforces their feeling right and superior. In their minds they "won". Take care of yourself first.
Third, you do not need to bring the subject up yourself. You can move on and flip the story from "I have to show you how full of --it the WT teachings are", to "I'm moving on and if you want to know why, ask me, but don't bother me with your JW nonsense". The first story sets you of to be victimized by their JW attacks. The second give you the control over your new believes, and to the fact that you really believe what you believe and there's no need to prove it to them. They will react a lot better (for you) to the second story than to the first one. Once they see that you mean business, they may attempt all kinds of passive/aggressive moves, but eventually will see that you mean business and leave you along. Then is when they might become interested in what you have to say.
