As I said in that post, "Hating yourself and/or feeling guilty about everything not only makes you miserable, it makes the rest of your family miserable as well, and can cause problematic, repetitive family behavior patterns to be passed down from one generation to another."
Nowhere is this more important than for parents who had physically, verbally, or sexually abused their children, or severely neglected them, when they were growing up. You know who you are. All the denial in the world will not change the fact that both you and the person or persons you abused know exactly what you did.
Parents who push their adult children away through cruel or unpleasant behavior (because of a sense that their children are better off without them), not only punish themselves, but do their children no favors either. By the same token, trying to make your children hate you through constantly accusing them of lying or by minimizing the significance of what you did will not make them feel better, but far worse. It accomplishes nothing but making them feel invalid and almost subhuman.
And you know, down deep, how much you really want them to love you and forgive you. And your children really do, deep down, want to forgive you. Please let them.
'Fess up to what you did directly to them and stop making excuses. Tell them how sorry you are even if that seems to make them angry or if they refuse to accept your apology. Tell them that you would like them to forgive you but you know you may not deserve it and you will certainly understand if they feel they cannot do so.
Try to explain to them the experiences that you had growing up that may have led you to do the foul deeds, but without using those explanations as a justification for your actions. There is no justification. Perhaps, in order to do this right, you will need a therapist to act as an arbiter between you and your adult children.
You always have three choices. First, you can deny what you did and continue to lie to everyone including yourself, but you will always know that it is true. Second, you can continually beat yourself up about it as if your shortcomings are written in stone and any harm you may have inflicted on your children is unforgivable and irreversible. The result of this course of self-damning action is continued guilt, which leads to more and more unpleasant feelings, which in turn lead to desperation, despair, and hopelessness.
Those two choices will not only make you feel worse, they will not help your children feel any better about you, your relationship with them, or their childhood. As I mentioned, it usually makes them feel much worse. If they have children themselves, the after-effects of what happened to them as children will continue to poison, in one way or another, their relationship with their own kids.
A much better course of action is to forgive yourself for your human frailties, learn from your mistakes so that you do not repeat them, and talk openly with your offspring as best you know how about what had happened and why you felt and acted the way that you did.
It's time to 'fess up. If you decide to do this, do not procrastinate. You might change your mind. There will never be a better time than right now. The transmission of dysfunctional family patterns from one generation to the next can be stopped.