Op I very much doubt that it occurred as a one off. I don't believe an otherwise loving, calm engaged parent randomly inflicted a truamatic act of violence on her child.
Don't get me wrong, I'm not accusing you of other acts of physical abuse, but your relationship with her must have had significant difficulties at the stage you snapped right? And presumably when you say ill you mean mentally unwell at that point right? So you were struggling, your parenting was suffering & then she experienced a truamatic act of violence from her primary care giver?
Yes that could defibately cause the mh difficulties she's experiencing now. Especially if geneticly at risk anyways.
I'm not perfect BTW. I have hit one of my kids once and pushed her another time. My kids have autism and other problems. At age two she head butted me so bad she shattered my nose and I pushed her v hard to stop her doing it a second time. She hit the back of the couch and her head hit the wall. Not badly I guess, so bump but shock and crying. The other time I was injured and lying down & she was kicking a bad bruise (that she caused) and I was holding her leg to stop her as I could move due to my injury. Her sister then bit my ear and I lost hold of her leg and slapped it hard instead when I was bit.
These are my mistakes, I was wrong. I was doing the best I could and I forgive myself but only because I faced up to it. I was v honest and apologised and sought more help and read more pa renting books and really none of it 'helped' much in yeschool of parenting, but taking respknsibility for it helped my relationship with her.
One of the most painful things I remember was my mother lying and saying she never hit me. She only hit me a few times but allways denied it. I needed my memories validated and I did not need her gaslight ing me claiming it never happended or it didn't harm me.
If my kids bring up my violent mistakes I will be honest, including if they talk about it public/in front of teachers or sw etc. It's not about the mistakes we make its how we deal with them that counts. She needs you to deal with this now by acknowledging her experience of this incident. Even if it causes you pain to face up to. And she's still hoping that you will, and she's still giving you the chance to repair things, but she won't hold out that hope forever. So step up now. Hiding from painful guilt won't help your daughter now, from her pov all that will mean is you don't love her enough to be honest with yourself. That's what she will take from this, unless you own up and truly accept how this made her feel.