To me there's two separate issue here, I'll address them separately.

First, the fact that you were supposed to disclose things like SI with your sister there or pushing you to answer things that you didn't want to. I'm not sure whether this is normal in family therapy, in one on one therapy it would be normal for the T to ask about it, but if you said you didn't want to answer (that goes for any question, not just SI), they should respect that. I'm also not sure how much is talked about private things in front of family members in such a setting, other users probably know better. But even in those settings, boundaries should always be respected, you do not have to answer any question you do not want to answer.

The second aspect to me is that she didn't really act properly about the whole issue. Making parents screen people for SI is as far as I know sometimes suggested, but I'd personally be very vary of that practice, it might work with people who only do it due to group pressure or something, but otherwise... I know that for me that would have been a disaster back when I lived with my parents.

Regardless of how she handled that whole topic, you say you don't want to go to see her again. That's fine, and actually quite common. Lots of people go to a therapist, who might have seemed like a good choice, but then they realize that either the therapist acts like this and it bothers them, or that there's literally anything under the sun that bothers them about it (could be the therapist is a smoker and that bothers you, could be they are acting inappropriately, could be you just don't click with them). It's recommended that in that situation, you try a different one. It seems to me that you'd like one on one therapy better, is that correct? If that's the case, can you ask somebody for a recommendation on a therapist for that? Or maybe also use something like PsychCentral, they have lots of therapists on there where you can look at their profile and all. But in that situation, most of the time the therapist will not take both you and your sister, that is not viewed as ethical usually. If you'd like family therapy together with your sister (which means both of you in one room, usually in that situation there is no or little one on one time), then I'd as well suggest you try to look for a different therapist, since no matter whether she has the right credentials and might be a good therapist for some people, for you she doesn't seem to be and that's all that counts.