Very well said. I concur with this entirely.Howdy!
Maybe something along the lines of;
I appreciate the opportunity to serve you with regards to the photographic shoot on such and such a date and address. I must however bring up an issue that is somewhat uncomfortable to discuss, as I certainly value our business relationship and would hate to have anything damage that relationship.
I have a policy of not working alongside other photographers unless I have a pre-existing relationship with them. I may employ methods and techniques that I do not wish to share with other photographers, as they provide me some of my competitive advantage. I only allow those on site whom are necessary for me to complete the assignment. I therefore must ask that no other photographers be present while I am working on this assignment.
I am quite certain that if you had a potential business competitor show up to your business you would be hesitant to give them free access to the inner workings of your business, or allow them to see your processes and procedures.
I am confident that as a business man, you understand my position.
I look forward to your positive response, and confirmation that we are still a go on such and such a date.
That's how I would do it - But - please consider not possibly throwing the baby out with the bath - Sometimes having a good strategic partner / photographer can be better for both of you. One of my best friends was a "competitor" - another commercial photographer ( Dennis, has it really been 20 years since we last talked? http://image2.findagrave.com/photos/...2517522339.jpg )
When we all lift each other up, we all come out ahead.
So, yes, I would let the client know - but I would be ever on the lookout for a mutually beneficial relationship. You never know where they will pop up. But they do take some time to develop.
Hope you find this helpful.