What Elizabeth says is also true. My daughter told her lie to a counselor in drug rehab, but to me, she denied saying it. She said that she had remained silent, so the counselor had drawn the wrong conclusion. She was lying to me too, though. I read her rehab daily journal (which the counselors read and write comments in) and it was obvious she was making a clear false claim.
Once they get away from the hateful parent for a while, sometimes the cloud clears and they admit the truth, ashamed of themselves for what they have done. I'm not so sure they are really the ones to blame though.
There are also cases of false memory implanted by repetitive questioning or descriptive suggestions, but that usually occurs in younger children. On the other hand, some accusations are valid and true and need to be taken seriously.
I believe that your sitation is more a matter of parental alienation causing desperate, irrational hate. As you alluded to, a key clue to the possible falsehood of an abuse claim is when the timing is too convenient toward an obvious motive.
My situation was similar. My daughter made her allegation so that she could live with her mom, according to what she was telling her friends on the internet. She has never expressed regret for her false accusation and we do not discuss it. Oddly, when the kids do it, they believe that it is a justified lie. My daughter seemed surprised that her friends were not impressed by her lie. I'm sure her mother was thrilled so D couldn't understand why her friends didn't agree.
My daughter recanted within a couple of weeks or less of the allegation, but it took a few months for them to drop the case. I was one of the lucky ones. She was separated from me most of the time, but being in rehab, she was also separated from her mother. Things could have been much worse.
If the girl is claiming she was 3 at the time, there are some credibility issues there. A 3 year old has very sketchy memory, if any memory at all. My earliest memory is at 4 years old. The little bit of memory a 3 yo may have can not be seen as reliable, since they can not distinguish fantasy from reality yet.
Also, at that age parents still need to bathe their children and may often see them naked. Not much likelihood that any of that is sexual in nature in any family. If there were really any probloem, why would it have had its beginning and ending at 3 years old? The story may soon crumble. The alienating parent is desperate to latch onto anything that could keep your H away from the kids, but she may expose that motivation in the process.
Has he ever shown any signs of DV to you? A tiger rarely changes his stripes, so if he was once an abuser, it is unlikely that he would have changed. If you see no signs of it, his x probably hasn't either.
Still, this is a monstrous problem that you have to take seriously. You don't always get a fair shake. I wish you luck. Get a lawyer. Can any family members on your H's side of the family, such as yourself, see and talk to the child?