AITAH if I don't tell husband the conversation I had with my 14yo daughter's therapist?

This is my first post her, so bare with me... to start I (34f) brought my 14yo daughter to therapy today (3rd session with this therapist). After her session she let me know she made another safety plan with her therapist ( she has done 3-4 plans in years prior with counselors etc.). She also mentioned they spoke about her last suicide attempt (hence creating a safety plan) and that her therapist would be calling me a little later. I calmly said okay, and asked gently when the last time was. She said it was last June and not recent, which was a relief. We went to other subjects after that and she went to her friends house when we got home. Fast forward an hour, and her therapist called me as expected. She reviewed the safety plan with me, she went over what my daughter said triggers her, her warning signs, what helps etc. Her therapist also let me know how many times and the ways my daughter disclosed she attempted suicide. I knew some of the attempts, but to hear how many and the ways devastated me. My daughter and I are extremely close. She is such a wonderful kid and I just can't wrap my head around why she wants to take her life when she has all the potential. She is smart, funny, athletic, social and all around a great person. She has so much insight, maturity and self awareness. But she is fragile, and emotional and my baby girl at the same time. So as I'm on the phone with the therapist we go over ways to respond to my daughter's warning signs, triggers, etc. We discuss great ways I can help my daughter in these tough times etc. The conversation was productive and I think some of the strategies will really help how my daughter copes with stress and negative things happening in her life. Now here is where I'm unsure on what to do... my husband (37m) was not on the phone call. As I said before we have had safety plans before. On the previous safety plans he is indicated as a trigger. The two of them argue about any and everything. I would call it more like bickering, and then I get stuck in the middle of it all the time. Most of the time it is about trivial topics. Sometimes I agree with my daughter when my husband says something I don't agree with (anything about women's rights, etc). Most of it is a battle of opinion. Anyways, when it is about a serious topic, my husbands response isn't the best. He doesn't yell, or call her names, but he does do a lot of lecturing and invalidating. He is more of a "do as I say, not as I do" parent. There is a definite power struggle between them. He also takes things personally, and if my daughter is struggling, he takes the opportunity to make it about himself ( if that makes sense). He often says things like "when I was a kid, I had to suck it up". I get he is trying to relate when he says some of these things, but sometimes the are so off topic and unrealatable to my daughters problem, it's is difficult to listen to. In these moments I'm often put in the middle by both of them. Even on my daughters safety plan she said to help mom can stick up for me to dad. Which I try to do, if she is in the right...sometimes she is being unreasonable. So I'm playing referee often. Anyways, I am ranting so I'll get to the point. I want to protect my daughter, and in the past when my husband has seen that she put him as a trigger, it upset him deeply. He took it very personally, and couldn't see how the way he communicates with her isn't the most effective. We have had many conversations about what he could say, or how to react in these moments together and with a family therapist. He is very receptive and makes it seem like he is willing to try something different, but then he doubles down on her behaviors. He'll start nitpicking everything she does, and as I said she truly is a great kid overall. But it is like, if she expresses dissatisfaction, he won't stop till she appears happy. Probably something he learned in his childhood. So now, here I am, with information about the well being of OUR daughter, and I do not want to talk to him about her new safety plan, or about the suicide attempts I just learned about. I don't want to talk to any of my friends or family about this either because I want to respect my daughters privacy. And the one person I can talk to about this, probably will make matters worse. So reddit, should I tell him, or keep this between me and my daughter?
Also, if anyone has advise on how I can support/ help my daughter more please feel free.