I had a client recently who was in tears feeling guilty over a bad decision she made about her child. I can remember feeling the same way over some decisions I made while raising my daughters. Parent guilt can be crushing!
Gently, she and I examined the situation and she was able to recognize her part and make a plan to apologize to her child. She was also able to let go of holding herself responsible for the circumstances that led to her decision that she was someone else's fault.
When we commit a crime and go before a judge, the judge is charged with helping render a decision that fits the crime and order punishment when warranted. If you have done something wrong, or had a part in something wrong, punishing yourself with massive guilt does not help anyone. That's like the judge throwing you in jail forever for forgetting a parking ticket.
We can't undo the past. Apologize sincerely and correct it if you can.
Then remove the noose. Parents are just humans who have children. It's a big job and we will make mistakes. Telling ourselves we are terrible parents is not helpful and wallowing in guilt will just keep us from moving forward.
And apologizing and making it right teaches your child that it's okay to make a mistake. That's a good lesson to learn.