To wonder if therapy work?

It’s probably worth giving both parties notice that you’d like to try having a break from it, give them a couple of weeks to work towards this and then see how things are without it. Then after 6 weeks or so see how your DD is.

Acceptance and commitment therapye, essentially learning to accept that bad things happen and negative emotions are part of the human condition. Helping your body feel them, experience them and then once you've gone through it continue on with a commitment to co tuning to live well with your own strong values. It's about getting to know yourself and your reactions and behaviours and having compassion for yourself when bad things happen

Had to look up one of review letters to remind myself ACT and CBT.

Only the initial appointments were spent dwelling on feelings and events and everything else was more about practically managing and reducing ongoing anxiety and living with the discomfort and fear which were based on real risk to life. It was incredibly helpful instead of everyone pussy footing around that my child was fine and had survived and much more helpful to basically say 'your child has a condition that has led to multiple life threatening medical emergencies and may continue to have more and could die young and the reality of the situation is you need to live with this the best way possible without being destroyed.

Therapy can help a lot, but it's quite possible for even longterm work to achieve virtually nothing, especially if the client (for whatever reason) feels that it's important to keep certain things secret, or to give a 'good' impression to the therapist rather than reveal what is really going on. Or perhaps the client/therapist connection never establishes.
It's very tricky to decide for someone else whether therapy is helping, and/or whether a different therapist would help more. You could ask her what she hopes to get out of it and really listen to the answer, then suggest she says that to the therapist next time.

Both the response from the therapist and DD don’t seem to be great indicators here.

The therapist should be much clearer about what the issues are and what they are doing. If DD just says “I guess” that sounds like she is trying to make you feel better about the effort you are putting in to it.

Perhaps ask if she knows what the therapist is trying to address with her? Ask if she thinks she should try a different therapist/approach? It may be this therapist is not great for her, it may also be therapy is not the solution.

In contrast with others I don’t think your DD is the best judge of if therapy is working. There are a lot if criticisms of the therapy industry, it can be quite the machine. Remember if some people will be pleased if you validate their feelings and decisions regardless of whether they are in their best interests.

It is worth having an outcome in mind for therapy, if someone is not functioning well are there specific areas you want to achieve something in?

If it is just a safe place for a teenager to speak to a neutral 3rd party that doesn’t need to be a therapist. Are there other older women in her life she can trust who she may be able to just talk through what is going on? They may be able to be more useful if it is a matter of issues in life that are getting to her.

Successful therapy particularly for dc does not need to be brutally challenging. They absolutely shouldn't look worn out at the end of session.
Dc and the therapist are the best sources of finding out if it is working for her.
Do you know what the goals for therapy are?
Therapy is a broad spectrum and works for some people much more than others as pp said.

I had therapy weekly for 6 months to help me get over PTSD from my son repeatedly almost dying during seizures and so much trauma around hospital stays and shocking treatment from medical professionals. I found it incredibly life changingky helpful. I started out with an open mind but also desparate because I was struggling with every aspect of my life. The first few sessions were talking about background and feelings but after that it was about finding ways to deal with resultant anxieties and avoidant behaviours that had come up, I had reading material around the behaviours and their root cause and what the changes I was being asked to make were hoping to achieve and it was like a finite journey back to being the capable woman I have always been.

If she's been improving while in therapy and happy to go I'd be inclined to believe it's having a positive impact

From someone that has recently been suffering with my mental health, I would be cutting tutors before I cut therapy.

I think it is tremendously helpful for some people and a complete waste of time/ money for others. Depends on multiple factors, including the therapist, the individual receiving therapy, the issues being addressed and the approach(es) being used to address them.

Nobody else's experience will tell you whether the therapy is actually helping your daughter.

Well, she needs to. Therapy done properly, with the right therapist, is brutally challenging. Do you see her immediately after the sessions? is she obviously tired? I was always absolutely sapped afterwards.

I'd suggest moving to fortnightly if you're struggling to cover the bills.

Have you actually asked her if she is finding it helpful?

Could you cut it to one a fortnight? Make savings elsewhere..