I would continue to look around for a therapist. Not wanting to meet Tuna at all seems very strange to me. Esp with the problems Tuna has. I don't know much about play therapy. We had many therapist suggest it until they met Wiz. He was astonishingly verbal at a very young age. We still spent at least at much time with the therapist as he did, but NO therapist was ever willing to treat us/him/the family with-o spending some time with him. Mostly they played games, but they talked while they did it, which was a good way to build rapport. Even the AWFUL therapist we saw who swore by Dr. Dobson's early books (when he advocated plentiful use of spanking) needed to spend some time with Wiz to try to see some of what we were dealing with.
Is there a children's hospital or developmental pediatrician around? The dev pediatrician would be able to suggest a good therapist or might have one on staff in the practice. A children's hospital will have an assortment of tdocs that could help you.
Who does her medications? If it is a child psychiatrist, call the office and ask if they have a therapist they refer people to. Don't forget about your insurance company. They may have a list of preferred providers that you can call. Make sure you are comfortable with the therapist. I normally went to the first appointment or two to give the history. Having a Parent Report is incredibly helpful. I often give it to the therapist on the second visit, or at the very end of the first. That gives me time to figure out if I like the doctor and think we can work together. A Parent Report is a document you create to keep ALL the info about your difficult child in one place. Copies of all or part of the report can be given to the people you are working with. You can find the outline on the FAQ/Board Help forum under the title Parent Input/Multidisciplinary Evaluation (MDE). It is amazingly helpful when communicating with the various docs and in keeping all of the info organized into a usable format.
Not all tdocs, or psychiatrists, will know about Ross Greene's book, but they should be willing to take a look at it. If you find one who is already familiar that is a very good thing. The therapist who helped us the most wasn't familiar but LOVED it after I gave her a copy. She learned about Love and Logic around that time and asked me to take a look at it and tell her my opinion. She wanted to know if I thought it was as useful as she thought it might be. I love L&L and it made a GIANT difference in my home, family and even my marriage. It is the ONLY parenting book that made sense to my husband and that he could implement and remember the techniques involved. For more info on L&L, visit
www.loveandlogic.com. With your family I would suggest Love and Logic Magic for Early Childhood. It is a birth to age 6 guide, but most difficult children are about 1/3 behind other chronologically aged kids. The website describes all of their books and might be very helpful.
As for if you are off base thinking that a therapist should work with parents in addition to kids, I would say no. Even in family therapy there are times when each person needs an individual session. I am not sure why this therapist sounds not quite right, but she does not sound like a good "fit" for you and your family. At any time that I have to change tdocs for any of us but husband, I make appts with several different tdocs. I go to the first appointments with each of them and then cancel any follow up appts with the ones that are not a good fit.