When abuse is eventually brought out into the open, the abused usually feels very resentful about the mother who SHOULD have seen the signs, but did nothing. Mom truns out to be shocked! "I had no idea!" But it doesn't happen in a vacuum, and there are plenty of warnngs that Mom ignores. Signs like the ones experienced now. I'm afraid this will be the case with you, and you'll find you had no "deep bond or telepathic connection" with her after all. By the way, ALL mothers think they have this so-called telepathy, especially with their first child. But it's clear something horrible is happening to her and you have no idea, despite your "telepathic bond".
I also believe you have some sexual misconceptions; sure, self-gratification feels good...but it doesn't feel THAT good until adolescence when the sex hormones kick in! When you breast-feed, the sexual feelings are all YOURS, as YOU have sex hormones; your baby doesn't yet have that feeling...just food and comfort. If you truly think the baby is sexually excited by being fed, this may be part of your problem! ("She wants me to touch her genitalia because it makes her feel especially good. This makes sense to me.")
Toddlers don't have the requisite sex hormones, either, though nerve endings make the body feel good when touched. So her behavior is clearly NOT NORMAL as you describe, to the exclusion of normal children's activities.
What is your husband's view on all this? You've conveniently left him out of the discussion, except to tell us of his face-slapping and compare it to your child's self-gratification issue in a way that is not clear! What was that little speech about "reparations" and forgiveness about in regards to your child's self-gratification? What "errors and reparation" are you referring to in regard to this issue? Doesn't make sense.
You keep making assertions, then denying them when pointed out...you clearly complained she wants to do this to the exclusion of all other activities in your first post, then claim it's not obsessive after describing obseesive behavior! You say you are with her "24/7" (which is impossible), then tell us about pre-school. You say "Last year she mentioned playing with another little girl and touching each other, and she said the name of the child was Anna", then you say "it is quite possible that some form of sexual play with other kids occurred at preschool. If this happened, I did not get any hint of it from her." You keep contradicting yourself!
"I would not, and I did not define her behavior as obsessive/compulsive and I will not take her to a professional."
You sound like an arrogant know-it-all first-time mother who needs to be "right", to the detriment of your own child.
I regret to say I must disagree with bluerose in that this is NOT the attitude of someone who cares about her daughter...and there is obviously not the "telepathic" connection you think there is or you wouldn't be writing about this looking for answers you don't want to hear.
Again, if she continues to act out, she will take a stranger's hand to her genitalia and if you're lucky, they will notify Mom. However, most likely she will encounter someone who take her up on her "offer", and she will be molested again. The perpetrator will claim "She WANTED it! She ASKED for it!" This is how child sexual abuse goes on and on, with the child acting out what she learned and attracting other molesters. God help her.