Girl I dated and slept secretly-with, from my former Gym has started coming to my new gym (After ghosting me for months. I tried twice to ask her out, and stopped contact)

I asked her out, thinking she was into me. she responds she is seeing someone and that It can be platonic. I said NO, and if she changes her mind to let me know, I don't want to be phony in that way

She still continues to come to the gym and is VERY flirtatious with my coach. There is chemistry developing there. Not sure how to handle this.

She messages me after the gym. 1/2 messages and respond back in a funny manner and the thread goes cold. And I don't try to "revitalize it"

I feel like she is trying to keep me in her orbit, while trying to seduce my coach (possibly), while she is moving in with her new boyfriend.

She is no-where close to being flirtatious with me.

This girl is hot, I don't feel like I'm sticking up for myself here. I'm nervous the she might hook-up with my coach I don't want that. (He has had a girl for 8 year much older then her).

I feel like she is using me, or keep me close to gather intel on the coach, so if her relationship goes sour with her current bf. She can get closer to Coach if she already hasn't.

Not sure what to do.