I am so sorry. I have escaped getting any DUIs, how, I don't know, but I know quite a few people without licenses here because of DUIs. Let them talk. EVentually, the gossip will die down. It always does. They will find someone else to talk about.
As for not driving - that is rough, especially when you have kids. Is there anyone you can trust to help? Maybe another parent whose kids are in the same activities who would be willing to take your kids along too for a little gas money?