I think it's a good thing you're trying a different therapist--this one may not be a good fit for you. Her being constantly late would really bother me, it would feel like she's unprofessional and unreliable and not respecting the client's time. I'd start every session angry with her and it wouldn't go well.

That said, it sounds like maybe you could take a bit more control over the conversation than you're doing, maybe? When she asks you about your week, you don't have to go over everything that happened if you don't want, you can just pick the one thing that seems most important to you. When she reflects back at you with something you just said, tell her it's not helpful to you. Maybe something to think about when you meet the new one.