Two thoughts: 1) from the tone of your post, I'm not sure you can just walk away from therapy, and 2) since you're facing a tough choice, why not give one more session a try, being honest - yes, I looked this stuff up, because I wanted to know more about you as I tell you my deepest secrets, etc. I mean, she doesn't believe your denials already, why not see what the direct approach gets you? If it doesn't go well, you can leave, and you'll have clarified the situation.

Oh, and 3) I don't see why she can't be effective knowing these things. I don't see that you crossed a boundary in looking stuff up - it's the baiting her with your knowledge that's the issue. Anything on the internet is fair game, and therapists should take more precautions if they don't want clients to see their laundry, dirty or clean.

I don't really have a similar experience - I don't want to know anything about my therapists because I need that blank wall - but I did find out something very surprising with No. 3. She was easily the most private of the three I've seen - I basically knew she was married and why she became a therapist. But then one day I ran into her at the locker room at the gym, and realized she had at least one kid (spotted a C-section scar) and you could have knocked me over with a feather. It impressed me with her level of professionalism in session (not so much the gym locker room), since most people can't avoid mentioning their kids. We never discussed that she had a kid, btw - I didn't see the point.

I guess I mention that because I wonder if learning this information had a positive impact on your view of your therapist. Do you admire what she's done with her personal life? If your relationship is already ambivalent and you don't trust her, and knowing about gay ex sugar daddy doesn't make you empathize with her, I think then it is time to find a new person.