I've thought a bit about your work thing. I wonder what lies behind your agreement to allow your competitor to shadow you? It is not clear to me that it is a reasonable or ethical request for your client to make as it seems to require you to share your work product with your replacement.
Unless your contract requires you to train your replacement or gives your client ownership over what I would have thought to be your own work product, I don't see how you would be morally or professionally obligated to share with the replacements.
I guess the client can have your competition attend the event. But that seems far different than requiring you to allow them to follow you around.
I've no idea what led to your decision to accept your client's request. Have you given any thought as to what boundaries will work for you to protect yourself professionally and emotionally? What are your boundaries? How will you share them? How will you respect them?
I would think it to be reasonable and professional to say: "I appreciate that you respect the value of my work and would like to carry through some aspects of my work as you switch to the competition. We will need to find a different way for that to happen. I find that it is inconsistent with my professional ethics and interests to have people from the competition shadow me or for me to try to train them at the same time I carry out the services for which we have a contract. Any such activity would interfere with my ability to provide excellent service and require me to share my work product with the competition. Of course, the competition is welcome to attend the event as guests, but it would be unprofessional for me to interact with them other than as guests during the event. I would be open to working with the competition on a fixed contract to help with the transition. We could negotiate the details of such an arrangement after the event if that is of interest."
Maybe you are so used to swallowing bitter pills that you've forgotten to ask yourself whether to take it to begin to avoid the nasty taste and stomach upset altogether....