Last word., kids turning the tables and TSG

How do you handle this situation:
You and your daughter come to a conclusion and next is “drop the subject”. You gently remind the daughter that a conclusion has been reached and it is time to drop the subject but they have to absolutely have the last word and so: Darling daughter says “If you say one more word then you will prove my point that it is you who are not dropping the subject.” SO, I stop talking and she, in her mind thinks that she “won” and has control of the situation.
This happens a lot where my daughters will turn the tables and use TSG on ME. I will tell them that they are not calm or dropping the subject or disagreeing appropriately and they will turn around and tell me that I am not calm or disagreeing appropriately or dropping the subject and when I open my mouth to speak, they say, “see, I told you.” They will tell me that since I am not calm or doing the skills that maybe TSG just isn’t for me and TSG isn’t working.
Sometimes I just stop talking, which feels a bit like them being the parent and my becoming the child and sometimes I respond, which then often becomes a power struggle. I feel like there are just no good options here. Can you help me? I am trying to focus on my behavior and roles, but it seems like the roles are constantly reversed and I don’t know how to get back to being a parent when they are using TSG wording on me and putting me in a “no win” situation.