Hello Emma,
First of all, {{{{{hugs}}}}} for your hurting mommy heart.
You made a mistake in slapping your difficult child, you have recognized your mistake and promised yourself not to do it again. You need to move on from that point, and stop beating yourself up. You cannot change the past, only the future, so take the lesson you have learned and apply it.
Now, with regard to the way in which the neighbours are treating you...DO NOT let them make you feel ashamed of yourself. You can't control what others do, but you CAN control how you react to it. If you walk around hangdog, then people will assume that you have something to feel ashamed of, and they will assume that the rumours are true.
If you walk with your head held high, then people may choose to dbelieve the gossip or not, but you are not contributing to their belief in it.
Here's something to think about...
My difficult child is currently in serious trouble with the law. He has a trial coming up in May, after which point, he may well end up in jail. And, the crime he allegedly committed took place at my neighbour's house. I mean right across the street. The police came, sirens blaring, cuffed him on our front lawn and dragged him off to the police station.
BUT I have nothing to be ashamed of, and I DO NOT hang my head in public. I still go out and about, say hello to my neighbours--even the ones at whose house this allegedly took place--and they say hello back, even those neighbours.
difficult child is responsible for his own behaviour and his own choices. I don't own those actions and I am not responsible for them. I have no reason to be ashamed because of difficult child's behaviour, because it's HIS behaviour, nott mine.
Please don't torture yourself, or feel ashamed on your difficult child's behalf. People will figure out his game eventually. But if you carry yourself with pride, you will be counteracting the gossip, not feeding into it.
Trinity