Dr's offices are not going to be very understanding about a 'double booking' - just tell her it is against HIPPA laws - confidentiality and all that. And then stop thinking about her issues and concentrate on yourself, this is a distraction ad will not help you on your journey.
Stop sharing your appointment dates with her, stop sharing the details, just say you are still thinking about some things and when you have a decision that is when you will share, then just keep that up.....she will get the message unless she is the type of person that requires a '2x4' upside the head, metaphorically speaking
You don't need this type of friend setting you up for issues.
Good luck.