My ex wife, six months ago allowed a 14 year old to drive my children and several other children around town. This resulted with the car in a ditch. Luckily no one was seriously injured. Although, it has left me worried to leave the kids alone with her. Is it possible for us to ask a jugde for supervised visits?

Sure it's possible. I'm assuming there was a police report of the incident. File a petition in Family Court for a change in visitation and present the police report as evidence.

Yes, you file for a modification of the current court order of custody and visits. You make the change that any visit with mother has to be supervised.