Hi Kim. I video a few of my clinics for my own personal/business use, but to-date have not allowed clients to film their sessions with me. One important question that comes to mind that I thought to ask, and that you may want to consider. How long have you been working with this client? The reason I ask is because generally speaking I try to keep my NEW client’s at-home workouts to the basics and to simple exercises that requires very little cueing or explanation. As we progress and they become more proficient with their program, then I would assign more complex exercise etc to them. So, ask yourself, “are the exercises that I am performing (and that my client is videotaping) simple exercises that I would be comfortable with him/her doing at home by themselves? Or, are these part of a program that I want them doing only with me until they become more proficient?) The answer to those questions may guide you to your answer about videotaping. In my opinion, sending my client home with exercises to do on their own at home is a tacit (or at least could be interpreted as) acknowledgement on my part as their trainer that I believe that they can safely perform the exercises. You need to feel fairly comfortable with that.
I hope that this helps.