This may or may not be the case, but to me this is irrelevant. What I see as a problem here is that she doesn't understand that she is not in a position to suggest you to get a second opinion.

Professionals normally don't refer customers to get a second opinion, no matter what their profession is. Doctors don't normally tell you to go to another doctor for a second opinion, and so don't mechanics, financial consultants..any specialist. It is upon you, as a consumer, to make a decision about getting a second opinion. The same with therapists.

As a professional, I make decisions to conduct my work in a certain way and you, as a client, decide if you accept it or if you want to get a second opinion and then decide which one you like better and which therapist you want to keep seeing. As a professional, I don't care how other professionals conduct their work. It's none of my business. If I need to consult with a colleague about a case, I'd just do that instead of sending a client to another professional. If a client of mine doesn't like what I do for whatever reason, they are free to either get a second opinion or to see a different therapist. But it is their decision, not mine. The power to make this decision resides within the client, not the therapist. Your T is attempting to take that power away from you by making this decision for you. By doing this she is engaging in a power struggle instead of trying to understand what the problem is between the two of you. Not smart on her part to say the least.

She is putting you and herself in the trap with no way out. Let's say you get a second opinion and it's different from hers? or the same as hers? So what? What does it change between the two of you? If you have a problem trusting her, getting a second opinion isn't going to change that. And if you don't have that problem and it's purely her imagination, then she needs to get a "second opinion" from a third party on how she conducts her work or better else she needs to get some therapy.

Frankly, this whole thing to me sounds like she feels insecure about her own competence and, instead of owning it, she projects it on you. If she needs a confirmation from another professional that she is on the right track and that she is doing a good work, she should own her self-doubts and get supervision or peer consultation instead of pretending that this is your problem by sending you to another professional.