I suggest that you do ask. As long as we do things with positive intentions, I believe we're entitled to ask anything we like of our therapists, and they are equally entitled to say they would rather not share, or to ask us why we would like to know. I think asking is perfectly reasonable in this situation, curiosity is human and a positive trait in my book, and so natural to want to know more about something so intriguing your T has mentioned repeatedly. Might give you some insight into how the EMDR worked for her and why too which you could consider regarding your own treatment.

I may be in the minority: many still like their therapists to be blank slates so they don't feel burdened by knowing difficult things about the therapist or that their therapist's needs are in the room, but I believe the therapeutic relationship often has a little room for some authentic personal sharing.