The only route to getting the school involved in a more serious way would be for you and your husband to present, with solid proof, an official complaint that the woman who works at the school (not sure she is a teacher there, don't think the OP has said?) has a conflict of interest between her job and her personal life.
As the affair is (apparently) over, such an accusation wouldn't in all probability hold water.
There is nothing in writing anywhere that says "a teacher shall not fuck a parent". There is a woolly "bringing the school into disrepute, affecting the job". Teachers are entitled to private lives as much as anyone, and if that involves fucking a parent, as long as it's off the premises and doesn't affect that teacher's job, then there is nothing you can use to warrant any kind of disciplinary action. The only slight chance of the school getting involved (and even then it would be a quite word in her ear, would be about the present giving. You can't stop someone trying to give someone else a present, no matter the motives. The teacher would be told "do it off the premises and watch your back, better still, don't do it at all"
I'm still at a loss as to how the situation got to the point where the OW told the deputy she had had an affair with the OP's husband. That sounds to me like she was actually giving him full disclosure. How did the OP ever know about that? The husband told her? Why? The OP's children have only just started at the school that this woman works at, so presumably when the affair happened, the OP's husband wasn't even a "child's parent at the school". He was just a bloke who fucked her.
Businesses are different and set their own rules.
The one guaranteed way to get this woman out of the OP's life is for the husband to tell her to fuck off, that she stands no chance, that he is not interested.