I'd like to weigh in if I may:

I don't think it's okay for him to just say no, cancel. You have already made the appointment and really you shouldn't even have to ask. He could have said "yes" and then brought up the issue and what he is perceiving to be happening after that. Or just have heard you'd seen her and mentioned it to you. As far as I know, lots of people in the US pay out of pocket, how would he even know for sure you're not seeing two people... I understand the risk for the client, but he hasn't set clear boundaries around R apparently and to suddenly enforce some he has with other clients isn't okay.

I can understand the part about not seeing two therapists at once, even if only sometimes, at least theoretically. I have set very clear boundaries with the two I'm seeing right now, flipper has gotten an okay to discuss anything, but should focus on my relationship. T has the same okay, but should focus on everything else, so trauma and so on. I think if you don't define stuff like this, it can lead to contradictions like one T recommends X and the other T doesn't, or also that the client tries to "play" with it, i.e. get one of them upset, talk to the other, kind of have both spaces interact. I don't think either of those things are particularly healthy.

I also think the thing now with R is going in that direction, though not badly. I can understand wanting to see her and so on, but to me it doesn't sound good if "whenever" you're upset you have a backup T that can hold that for you. Because realistically, there's gonna be a time where there's nobody around. And you have to be able to work through that on your own, even if for just a little while. Of course it's okay to sometimes do that, but learning to rely on yourself is a skill too.

But those things are to be discussed before starting such a thing, not when he notices how he doesn't like a certain aspect of it. It sounds to me like he didn't give it a lot of thought at the time...

Also, just as an aside, but a T randomly calling is rather unsettling. Only the forensics guy has ever done that to me (and I'm starting to think maybe he just accidentally put down the wrong major and wanted to get into crime scene analysis or smth) and even if you have no issues with them, it's anxiety inducing. T thankfully always texts me first. We by the way also have it set up so I always call him, meaning I pay the bill. The only time he has ever called me (except for scheduling at the beginning) was about his cancer.