Variances are granted IF no complaints or concerns are found. Many times, variances include posting the variance request for some number of houses around the property requesting it. So this will allow the neighbor(s) in question to speak against the variance as well as seek support from others. And sometimes it does not take much to get people to sign a petition when fear is thrown in. And from my experience, if any objections are brought forth, the variance is denied. The township board is not going to or will want to, assume responsibility or liability for future problems AFTER requesting a variance be granted when open concern is brought forward. Chances are that 99% of such matters will be denied.
Personally, I think I'd be looking for another home. Studies have shown that a good number of molesters have also been molested, and come families with serious problems. Everything from child abuse, to drugs, to cruelty to animals. The son may be locked up, but the family, and the actions of the other family members should put up a red flag. There is no doubt a connection with the son's problems that landed him in jail, and the family as a whole. I would like to say you should move due to being able to keep bees in peace, but feel that other concerns are warrented.