Reputation is ruined by gossip

I live in extremely small community. Where everybody is acquaintances or friends.I can tell that something is being said about me because every time I drop my kid off at school nobody will say hi to me or talk to me. And I really don't know how to handle it? Do you hold your head up high and still say hi. Or do I just ignore everybody and act like they're not there. and I know I'm not doing anything wrong because I just sit at my house with my kids and my husband. Gossip has gotten so bad people I don't even know are giving me the side-eye and giving me weird looks. And I do know who is spreading the rumors it's an ex friend who also works at the school district. She's spreading around that I slept with her husband but I did not and I told her the several times.I'd love some advice on how to handle the situation!