as long as you are not calling it Turning Stone or very similar, running it with the intention to benefit off of an established tournament by somebody else, you should be good. Same days might be an issue - for you and others. But if it's the Fairfield Inn Open across the road on the days/weekend before or after, that should be okay. Bring it on!
I get what you mean. Nobody wants to loose players to somebody else. Putting things close to each other (location and timing) should benefit everybody. That's what's happening right now in September in the Northeast: Turning Stone, Raxx MVP Open,Connecticut Open, US Open. That's what you want, everybody benefiting from each other. There is even a (slightly) "smaller" 10-Ball Open at Raxx, which sneaked in and is benefitting as well, without colliding. Not sure how this came along in detail, but those guys are talking and coordinating, I guess.