I would think the therapist would talk to you first as part of the regular appointment. If your daughter gets angry, it's up to the therapist to handle that. You should not avoid going in because she's ticked off, but you shouldn't tell her up front that you're going to talk to the counselor without her. Sometimes a child will accept a comment from the doctor or therapist ("I'm going to have you wait in the waiting room while I talk to Mom for a few minutes") that they won't accept from Mom, or sometimes the therapist can advise the parent on what to say.
Re email: I don't think it's possible for all the info about the past 3 weeks to go into an email anyway, and doctors/therapists would spend forever just reading long explanations or background with no opportunity to ask questions. Moreover, putting stuff out on an email that can be misdirected or misfiled is a bad idea! Or, you can make an appointment on your own (which you would pay for) - the therapist can't take time from other clients to do a whole lot of unpaid work. I do think it's okay to leave a voice mail asking what the process is for communicating in between appointments.
I think it's too bad there was a 3-week window between appointments but I think it's just not feasible to wait until the "day off" to fill in the therapist on 3 weeks of events/occurrences! I'm sure they are relevant but how much can you cram in on the "day of"?? I don't think you have to expect the doctor to accomplish as much in the 2nd appointment - right now the goal is to get your child to feel comfortable, and if she doesn't do a lot of talking, that's normal.
Try not to get exasperated - this is only the second appointment.
Also try to schedule a bunch of appointments, every week or every two, whatever you and the therapist think, so you aren't stuck every week trying to find out what's available. That's why you had a 3 week wait - everyone else had booked up the available times! Ask the therapist how many appointments you should make - probably 4-6 is the right answer. If you don't need them, you can cancel in plenty of time to not get charged and to let the therapist fill those with other clients. But most things don't get solved in 2-3 sessions, so it's probably wise for you to book a bunch right now.
Good luck and I hope the sessions are fruitful.