If your last therapy experience was intentionally short-term, I'd be inclined to guess that the therapist was more cognitive-behavioral - but it's difficult to tell just from that example.
I'd be wary too, in your position. There's nothing to stop any therapist from checking all of the boxes in their Psychology Today profiles - so if you do start looking for a new therapist, it's perfectly acceptable (and should be encouraged) to call and ask questions before setting up a first appointment. Don't feel self-conscious about this - consider this the due diligence necessary to choose a therapist, on the same level as merely googling another type of medical provider!
If I were you, I'd give the therapist one more chance - see what the next session is like, now that she's seen an example of how your family interacts with you. It's possible that she really just didn't understand the severity of the situation at first - but after reading that email, alarm bells should be going off in her head! Hopefully she'll be more prepared for the next session.
However, I'm honestly not too hopeful, based on the apparent incredulity that you described - I'm still very early in my career, and I've already had a lot of experience with severe personality disorders. I haven't gone out of my way looking for this experience, either - it's just that an incredibly high percentage of individuals who seek out therapy either have a personality disorder or were raised by individuals with personality disorders! If I were in your therapist's position right now, I'd think "oh shit, I screwed up and completely misunderstood the situation," and would probably tell the client, "I'm sorry, I misunderstood at first, but now I understand what you're talking about. Ignore everything I just said; let's start again." I'd completely switch gears - but I'd do so confidently, because I have previous experience helping people with typical relationship difficulties and with severe personality dysfunction. If your therapist was shocked to the point that her jaw dropped and she literally had no words to describe her surprise, then she likely doesn't have as much experience treating personality disorders as she thinks she does. At the very least, maybe she stereotyped you, thinking that you appeared to be too emotionally stable/successful/high-functioning/etc. to have been raised in such a dysfunctional environment - but if that's the case, she needs to work on her poker face! It's usually not a good idea to react with shock to what a client is saying (although in this case, it sounds like it was at least incredibly validating, considering the fact that you felt so misunderstood at first!).
Anyway, usually when therapists advertise that they're experienced in treating personality disorders, they're including NPD and BPD in that description. OCD is actually an anxiety disorder, not a personality disorder (there is, however, an Obsessive Compulsive Personality Disorder - OCPD - but that's completely different, and most people have never heard of it!). As I mentioned above, don't worry about potentially "firing" this therapist if she doesn't seem to have the experience you need, and don't feel bad about calling to "interview" other therapists in order to find a good fit!