I know how it hurts with your W looking at places. After your recent conversation, you may be a little more ambivalent toward it. My W wanted my feedback on places, and I actually looked at places with her. It kind of cuts both ways TBH. It's freeing from the drama on one hand. OTOH you miss your W.
It sounds to me with your most recent conversation, a firm co-parenting plan would be in order. Really, it's for both your benefit and hers.
I see a lot of fear coming from her in that conversation. Fear is a horrible guide, but it's a powerful motivator.