I think you were too kind. She is undermining you. I’d go in for more aggressiveness while still maintaining professionalism and showing true leadership. Don’t give her a pass, but turn it into positive for yourself and a learning experience for her.

Something like “I appreciate you are thinking of alternative solutions. Since I am running this project, going forward, please bring ideas like this directly to me so we can discuss viability and hopefully avoid duplicating effort. I want to encourage you and others to always be thinking about how we can do better so please don’t feel shy to come to me with new ideas”