You asked about your sister and the chizuk you can give her. You may want to discuss this with someone who can give you clarity based on the specifics, but let me just provide some general ideas. Certainly listening to your sister and understanding her feelings is already so much. What else are sisters for, and who else can be as understanding as you can?
However, listening and understanding shouldn’t morph into giving advice, and you should certainly not encourage her to flout her parents’ wishes or imply in any way that you support her doing things that you know will upset your parents. I would assume that you don’t feel that you should be rebuking her or educating her, yet it’s also not your place to advise her in her decisions and encourage anything that might be questionable. Doing so would be very wrong and would also make the situation much worse — between your sister and her parents, and perhaps also between you and your parents.
It’s possible that, seeing the changes you have made in your life, your parents are coming down much harder on your sister out of their fear that she will go the same way. This is just one more reason to be careful with what you do and say, because if your parents ever sense that you are encouraging her, their fears will actually be confirmed.
In general, there’s no need at all to offer that kind of “encouragement” in order to give your sister chizuk. Offering a listening and non-judgmental ear should be helpful enough.
