I'm also feeling puzzled even tho I see that you are a church preschool director. I don't understand why that would put your son's lives in the spot light. Do you mean they are looking at them to see if you raised them right and therefore you know how to be a preschool director? Is the preschool a private school that's open everyday or a Sunday School? If it's open everyday can the public also use it?
My granddaughter went to a church preschool and I didn't see anyone criticizing the director or her children. Even tho we weren't church members I felt a family like atmosphere in which everyone was included.
I was raised in fundamental churches and I do remember some people in the church being critical of the teenagers. And my response then as it is now is "so what?" If I know that I'm OK in God's eyes it doesn't matter what anyone else thinks.
Is it possible that you are being overly sensitive? Since you know that your sons are good kids, treat them just as any mother would treat their good sons. Forget other's criticisms. And if someone is voicing criticism to you, try to ignore it but if you can't, tell them that you have good sons and do not agree with their assesment. Or even that you don't wish to discuss your sons' behavior.
If your position is contingent on your sons behaving in a certain way (if being law abiding is not sufficient), I say that it's not worth keeping. Family comes first.
Whether or not the church keeps you as preschool director should depend only on your qualifications. Whether or not you stay should depend on whether or not you want the job. How your sons behave has no relationship to it.
And if you can believe that, then you can help your sons to learn to not let criticism unduly bother them.
"Let him who is without sin cast the first stone." comes to mind. And I strongly believe that church is about showing Christ's love. Picking anyone apart is not loving. And if church members are being overly critical I would suggest discussing this with your minister.