I would actually try this new T if she does EMDR, because you're in the middle of treatment that includes that. You are under no obligation to stay with her. She could be an awesome fit for you and feel comfortable fairly early. And passing general info from one T to another can be useful, it's happening for me now. Something is clearly off with your T's behavior.
What she's doing is most likely not aimed at you, it's probably what happens everywhere in her life. But that doesn't much soften the annoyance factor or frustration or experience of being disrespected. ADHD and OCD are linked with chronic lateness or chronic lateness syndrome. I've had a couple friends who are so affected and it costs them relationships for sure. Passive aggressive behavior can also cause such lateness but, yeah, let's hope it's not that.
Assert your thoughts on this to her. You don't have to be rude or aggressive but it would be healthy to be able to be honest and tell her how it makes you feel. That is the minimum I'd suggest.