Is it permissible for a wife to deny her husband intimacy if he molested one of their children and she became repulsed by him, yet she continues to live with him for the sake of the children?

It is not permissible for a wife to deny her husband his right to the bed as long as he provides for her reasonably, unless there is an excuse. The husband's committing sins is not a justification for denying him his right. If the husband repents sincerely, the wife should forgive him. If he has not repented, then the wife should strive to reform him and help him to repent and become upright. If that does not work, then she should weigh between staying with him or separating from him, choosing the lesser of two harms.