You have 3 separate actions that you can take.
1. Restraining order. It appears that this neighbor is harassing you by calling the police, accusing your children, and threatening you. It may be a good idea for you to file for a restraining order against him so that he leaves your family in peace. If he continues to contact you, you may then call the police yourself and have the courts fine him and possibly jail him for contempt of court.
2. Defamation. You may try to file a civil suit for defamation, but those are relatively hard to win. To have a "prima facie
" (valid/good on it's face) case for defamation you must show 4 things:
a) That a defamatory comment or comments
b) Were made that were about or concerning the plaintiff (your kids, who you will represent as guardian)
c) These comments were made to third parties AND
d) the plaintiff experiences damages or injury through those words.
If the person believed that what they were telling is truth, or it was an opinion, it is very hard to win.
3. Insurance fraud. If, however, you have proof that no damage was committed to your neighbor's property and he claimed it anyway, then you very well can contact his insurance company and have them do an investigation for insurance fraud. If guilty, your neighbor may be guilty of a felony and can be federally charged under "mail fraud statutes". This is the link to the CA Dept of Insurance if you decide to contact them:
Dimitry Alexander Kaplun, Esq.