I think to label this incident about a lack of empathy and improper support is to oversimplify the wide range of upsetting situations clients bring to T's and how they can respond in many ways that are supportive.

First you have to look at the upsetting situation for which you sought support. What you faced was something that probably almost all parents face on a regular basis, if not occasionally. I don't know if your child is normally cooperative or if you don't have the task of usually getting her off to school, but certainly all kids, particularly teenagers, can refuse and be obstinate at times. And if you're committed to being a loving parent, which I believe that you are, then engaging their cooperation without violence or threats can be a challenge.

So I would wonder why the big reaction to a child's lack of cooperation-- it suggests that there is something more to it than just being upset that it was difficult to do? I speculate that you were over the top upset that your bossing around strategy, which you use with other people in your life who back down in response, didn't work with your daughter, and you had little else to work with. So what you sought support for was your unhappiness that you couldn't boss your child around and have the outcome be what you wanted it to be. And your T tried to get you to focus on the things that you can control and perhaps to understand that parenting for the purpose of bossing your kid around might not be the best way to enhance your relationship with her. Maybe she wanted you to feel that it was okay to not be able to control your child (or anyone else, like her maybe?), that your world wouldn't end, that you'd still be the same powerful person with all the same competent and loveable qualities even if someone refuses to be bossed around by you.

I think asking for empathy and support for dysfunctional behavior is unlikely to get you anywhere with a good T. Sometimes I get a clue for what my more hidden dysfunctions are by observing my reaction to what others say to me. If I am unhappy about what people are giving me, or it makes me feel angry, then I look more closely at what the situation and my response was. Sometimes it is just that I have different values than other people, and it's not about dysfunction. Most of the people in my life, for instance, are not supportive when it comes to me skipping medical exams that are "protocol" for the particular disease that I was diagnosed with. I say an exam around 6 months is not meaningfully different than a 3 month one, and I am a bit more skeptical about the value of medical intervention compared to the average person.

As other people have pointed out, you insist on looking at this situation as a failure of your T. You refuse to consider the possibility that what you feel reveals something about your own failure. You've obviously chosen a T who is not a doormat and doesn't roll over and agree with you whenever you bark at her. So you can either decide it's not worth the effort for you to change or you can try to change and see if there are positive benefits in your relationships with other people who refuse to be bossed around by you.