I think it is odd the therapist would mention much about their daughter too without there being some reason.

I have not had a situation where I thought a therapist would be better than my own parents. Usually I wonder if their offspring are as screwed up as I imagine them to be after being raised by such whackos as I find therapists to be. The friends I have whose parents are therapists certainly are not unscrewed up. The therapists I know as friends are not without their issues with their children. I don't have children and did not like being one and family stuff is not a big thing with me. Usually when the therapist mentions their family at all to me - I just ask why she is telling me about it. Usually her response has been to admit there is nothing therapeutic in her revelations, just that she thought I would find it interesting. Shocking sometimes how little she knows me.